Search results for: rate of convergence
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 8257

Search results for: rate of convergence

8257 Statistical Convergence of the Szasz-Mirakjan-Kantorovich-Type Operators

Authors: Rishikesh Yadav, Ramakanta Meher, Vishnu Narayan Mishra

Abstract:

The main aim of this article is to investigate the statistical convergence of the summation of integral type operators and to obtain the weighted statistical convergence. The rate of statistical convergence by means of modulus of continuity and function belonging to the Lipschitz class are also studied. We discuss the convergence of the defined operators by graphical representation and put a better rate of convergence than the Szasz-Mirakjan-Kantorovich operators. In the last section, we extend said operators into bivariate operators to study about the rate of convergence in sense of modulus of continuity and by means of Lipschitz class by using function of two variables.

Keywords: The Szasz-Mirakjan-Kantorovich operators, statistical convergence, modulus of continuity, Peeters K-functional, weighted modulus of continuity

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8256 Statistical Convergence for the Approximation of Linear Positive Operators

Authors: Neha Bhardwaj

Abstract:

In this paper, we consider positive linear operators and study the Voronovskaya type result of the operator then obtain an error estimate in terms of the higher order modulus of continuity of the function being approximated and its A-statistical convergence. Also, we compute the corresponding rate of A-statistical convergence for the linear positive operators.

Keywords: Poisson distribution, Voronovskaya, modulus of continuity, a-statistical convergence

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8255 Evaluation of Quasi-Newton Strategy for Algorithmic Acceleration

Authors: T. Martini, J. M. Martínez

Abstract:

An algorithmic acceleration strategy based on quasi-Newton (or secant) methods is displayed for address the practical problem of accelerating the convergence of the Newton-Lagrange method in the case of convergence to critical multipliers. Since the Newton-Lagrange iteration converges locally at a linear rate, it is natural to conjecture that quasi-Newton methods based on the so called secant equation and some minimal variation principle, could converge superlinearly, thus restoring the convergence properties of Newton's method. This strategy can also be applied to accelerate the convergence of algorithms applied to fixed-points problems. Computational experience is reported illustrating the efficiency of this strategy to solve fixed-point problems with linear convergence rate.

Keywords: algorithmic acceleration, fixed-point problems, nonlinear programming, quasi-newton method

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8254 A Research Analysis on the Source Technology and Convergence Types

Authors: Kwounghee Choi

Abstract:

Technological convergence between the various sectors is expected to have a very large impact on future industrial and economy. This study attempts to do empirical approach between specific technologies’ classification. For technological convergence classification, it is necessary to set the target technology to be analyzed. This study selected target technology from national research and development plan. At first we found a source technology for analysis. Depending on the weight of source technology, NT-based, BT-based, IT-based, ET-based, CS-based convergence types were classified. This study aims to empirically show the concept of convergence technology and convergence types. If we use the source technology to classify convergence type, it will be useful to make practical strategies of convergence technology.

Keywords: technology convergence, source technology, convergence type, R&D strategy, technology classification

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8253 A Case Study on the Long-Term Stability Monitoring of Underground Powerhouse Complex Using Geotechnical Instrumentation

Authors: Sudhakar Kadiyala, Sripad R. Naik

Abstract:

Large cavern in Bhutan Himalayas is being monitored since the construction period. The behavior of the cavern is being monitored for last 16 years. Instrumentation includes measurement of convergence of high walls by geodetic monitoring, load on the support systems with load cells and instrumented bolts. Analysis of the results of instrumentation showed that during the construction period of the cavern, the convergence of the cavern varied from 181 - 233 mm in the unit bay area with maximum convergence rate of 2.80mm/day. Whereas during the operational period the total convergence observed was in the range of 21 to 45 mm during a period of 11.30 years with convergence rate of 0.005 to 0.011 mm/day. During the last five years, there were no instances of high tensile stress recorded by the instrumented bolts. Load on the rock bolts have shown stabilization trend at most of the locations. This paper discusses in detail the results of long-term monitoring using the geotechnical instruments and how the data is being used in 3D numerical model to confirm the stability of the cavern.

Keywords: convergence, displacements, geodetic monitoring, long-term stability

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8252 Improving the Performance of Back-Propagation Training Algorithm by Using ANN

Authors: Vishnu Pratap Singh Kirar

Abstract:

Artificial Neural Network (ANN) can be trained using backpropagation (BP). It is the most widely used algorithm for supervised learning with multi-layered feed-forward networks. Efficient learning by the BP algorithm is required for many practical applications. The BP algorithm calculates the weight changes of artificial neural networks, and a common approach is to use a two-term algorithm consisting of a learning rate (LR) and a momentum factor (MF). The major drawbacks of the two-term BP learning algorithm are the problems of local minima and slow convergence speeds, which limit the scope for real-time applications. Recently the addition of an extra term, called a proportional factor (PF), to the two-term BP algorithm was proposed. The third increases the speed of the BP algorithm. However, the PF term also reduces the convergence of the BP algorithm, and criteria for evaluating convergence are required to facilitate the application of the three terms BP algorithm. Although these two seem to be closely related, as described later, we summarize various improvements to overcome the drawbacks. Here we compare the different methods of convergence of the new three-term BP algorithm.

Keywords: neural network, backpropagation, local minima, fast convergence rate

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8251 A Fast Convergence Subband BSS Structure

Authors: Salah Al-Din I. Badran, Samad Ahmadi, Ismail Shahin

Abstract:

A blind source separation method is proposed; in this method we use a non-uniform filter bank and a novel normalisation. This method provides a reduced computational complexity and increased convergence speed comparing to the full-band algorithm. Recently, adaptive sub-band scheme has been recommended to solve two problems: reduction of computational complexity and increase the convergence speed of the adaptive algorithm for correlated input signals. In this work the reduction in computational complexity is achieved with the use of adaptive filters of orders less than the full-band adaptive filters, which operate at a sampling rate lower than the sampling rate of the input signal. The decomposed signals by analysis bank filter are less correlated in each sub-band than the input signal at full bandwidth, and can promote better rates of convergence.

Keywords: blind source separation, computational complexity, subband, convergence speed, mixture

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8250 A Subband BSS Structure with Reduced Complexity and Fast Convergence

Authors: Salah Al-Din I. Badran, Samad Ahmadi, Ismail Shahin

Abstract:

A blind source separation method is proposed; in this method, we use a non-uniform filter bank and a novel normalisation. This method provides a reduced computational complexity and increased convergence speed comparing to the full-band algorithm. Recently, adaptive sub-band scheme has been recommended to solve two problems: reduction of computational complexity and increase the convergence speed of the adaptive algorithm for correlated input signals. In this work, the reduction in computational complexity is achieved with the use of adaptive filters of orders less than the full-band adaptive filters, which operate at a sampling rate lower than the sampling rate of the input signal. The decomposed signals by analysis bank filter are less correlated in each subband than the input signal at full bandwidth, and can promote better rates of convergence.

Keywords: blind source separation, computational complexity, subband, convergence speed, mixture

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8249 L1-Convergence of Modified Trigonometric Sums

Authors: Sandeep Kaur Chouhan, Jatinderdeep Kaur, S. S. Bhatia

Abstract:

The existence of sine and cosine series as a Fourier series, their L1-convergence seems to be one of the difficult question in theory of convergence of trigonometric series in L1-metric norm. In the literature so far available, various authors have studied the L1-convergence of cosine and sine trigonometric series with special coefficients. In this paper, we present a modified cosine and sine sums and criterion for L1-convergence of these modified sums is obtained. Also, a necessary and sufficient condition for the L1-convergence of the cosine and sine series is deduced as corollaries.

Keywords: conjugate Dirichlet kernel, Dirichlet kernel, L1-convergence, modified sums

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8248 Random Walks and Option Pricing for European and American Options

Authors: Guillaume Leduc

Abstract:

In this paper, we describe a broad setting under which the error of the approximation can be quantified, controlled, and for which convergence occurs at a speed of n⁻¹ for European and American options. We describe how knowledge of the error allows for arbitrarily fast acceleration of the convergence.

Keywords: random walk approximation, European and American options, rate of convergence, option pricing

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8247 Covariance of the Queue Process Fed by Isonormal Gaussian Input Process

Authors: Samaneh Rahimirshnani, Hossein Jafari

Abstract:

In this paper, we consider fluid queueing processes fed by an isonormal Gaussian process. We study the correlation structure of the queueing process and the rate of convergence of the running supremum in the queueing process. The Malliavin calculus techniques are applied to obtain relations that show the workload process inherits the dependence properties of the input process. As examples, we consider two isonormal Gaussian processes, the sub-fractional Brownian motion (SFBM) and the fractional Brownian motion (FBM). For these examples, we obtain upper bounds for the covariance function of the queueing process and its rate of convergence to zero. We also discover that the rate of convergence of the queueing process is related to the structure of the covariance function of the input process.

Keywords: queue length process, Malliavin calculus, covariance function, fractional Brownian motion, sub-fractional Brownian motion

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8246 Convergence Analysis of a Gibbs Sampling Based Mix Design Optimization Approach for High Compressive Strength Pervious Concrete

Authors: Jiaqi Huang, Lu Jin

Abstract:

Pervious concrete features with high water permeability rate. However, due to the lack of fine aggregates, the compressive strength is usually lower than other conventional concrete products. Optimization of pervious concrete mix design has long been recognized as an effective mechanism to achieve high compressive strength while maintaining desired permeability rate. In this paper, a Gibbs Sampling based algorithm is proposed to approximate the optimal mix design to achieve a high compressive strength of pervious concrete. We prove that the proposed algorithm efficiently converges to the set of global optimal solutions. The convergence rate and accuracy depend on a control parameter employed in the proposed algorithm. The simulation results show that, by using the proposed approach, the system converges to the optimal solution quickly and the derived optimal mix design achieves the maximum compressive strength while maintaining the desired permeability rate.

Keywords: convergence, Gibbs Sampling, high compressive strength, optimal mix design, pervious concrete

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8245 Adaptive Filtering in Subbands for Supervised Source Separation

Authors: Bruna Luisa Ramos Prado Vasques, Mariane Rembold Petraglia, Antonio Petraglia

Abstract:

This paper investigates MIMO (Multiple-Input Multiple-Output) adaptive filtering techniques for the application of supervised source separation in the context of convolutive mixtures. From the observation that there is correlation among the signals of the different mixtures, an improvement in the NSAF (Normalized Subband Adaptive Filter) algorithm is proposed in order to accelerate its convergence rate. Simulation results with mixtures of speech signals in reverberant environments show the superior performance of the proposed algorithm with respect to the performances of the NLMS (Normalized Least-Mean-Square) and conventional NSAF, considering both the convergence speed and SIR (Signal-to-Interference Ratio) after convergence.

Keywords: adaptive filtering, multi-rate processing, normalized subband adaptive filter, source separation

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8244 Effect of Structural Change on Productivity Convergence: A Panel Unit Root Analysis

Authors: Amjad Naveed

Abstract:

This study analysed the role of structural change in the process of labour productivity convergence at country and regional levels. Many forms of structural changes occurred within the European Union (EU) countries i.e. variation in sectoral employment share, changes in demand for products, variations in trade patterns and advancement in technology which may have an influence on the process of convergence. Earlier studies on convergence have neglected the role of structural changes which can have resulted in different conclusion on the nature of convergence. The contribution of this study is to examine the role of structural change in testing labour productivity convergence at various levels. For the empirical purpose, the data of 19 EU countries, 259 regions and 6 industries is used for the period of 1991-2009. The results indicate that convergence varies across regional and country levels for different industries when considered the role of structural change.

Keywords: labor produvitivty, convergence, structural change, panel unit root

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8243 Convergence Analysis of Training Two-Hidden-Layer Partially Over-Parameterized ReLU Networks via Gradient Descent

Authors: Zhifeng Kong

Abstract:

Over-parameterized neural networks have attracted a great deal of attention in recent deep learning theory research, as they challenge the classic perspective of over-fitting when the model has excessive parameters and have gained empirical success in various settings. While a number of theoretical works have been presented to demystify properties of such models, the convergence properties of such models are still far from being thoroughly understood. In this work, we study the convergence properties of training two-hidden-layer partially over-parameterized fully connected networks with the Rectified Linear Unit activation via gradient descent. To our knowledge, this is the first theoretical work to understand convergence properties of deep over-parameterized networks without the equally-wide-hidden-layer assumption and other unrealistic assumptions. We provide a probabilistic lower bound of the widths of hidden layers and proved linear convergence rate of gradient descent. We also conducted experiments on synthetic and real-world datasets to validate our theory.

Keywords: over-parameterization, rectified linear units ReLU, convergence, gradient descent, neural networks

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8242 Lambda-Levelwise Statistical Convergence of a Sequence of Fuzzy Numbers

Authors: F. Berna Benli, Özgür Keskin

Abstract:

Lately, many mathematicians have been studied the statistical convergence of a sequence of fuzzy numbers. We know that Lambda-statistically convergence is a kind of convergence between ordinary convergence and statistical convergence. In this paper, we will introduce the new kind of convergence such as λ-levelwise statistical convergence. Then, we will define the concept of the λ-levelwise statistical cluster and limit points of a sequence of fuzzy numbers. Also, we will discuss the relations between the sets of λ-levelwise statistical cluster points and λ-levelwise statistical limit points of sequences of fuzzy numbers. This work has been extended in this paper, where some relations have been considered such that when lambda-statistical limit inferior and lambda-statistical limit superior for lambda-statistically convergent sequences of fuzzy numbers are equal. Furthermore, lambda-statistical boundedness condition for different sequences of fuzzy numbers has been studied.

Keywords: fuzzy number, λ-levelwise statistical cluster points, λ-levelwise statistical convergence, λ-levelwise statistical limit points, λ-statistical cluster points, λ-statistical convergence, λ-statistical limit points

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8241 Homogenization of a Non-Linear Problem with a Thermal Barrier

Authors: Hassan Samadi, Mustapha El Jarroudi

Abstract:

In this work, we consider the homogenization of a non-linear problem in periodic medium with two periodic connected media exchanging a heat flux throughout their common interface. The interfacial exchange coefficient λ is assumed to tend to zero or to infinity following a rate λ=λ(ε) when the size ε of the basic cell tends to zero. Three homogenized problems are determined according to some critical value depending of λ and ε. Our method is based on Γ-Convergence techniques.

Keywords: variational methods, epiconvergence, homogenization, convergence technique

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8240 A Survey on Fixed Point Iterations in Modular Function Spaces and an Application to Ode

Authors: Hudson Akewe

Abstract:

This research presents complementary results with wider applications on convergence and rate of convergence of classical fixed point theory in Banach spaces to the world of the theory of fixed points of mappings defined in classes of spaces of measurable functions, known in the literature as modular function spaces. The study gives a comprehensive survey of various iterative fixed point results for the classes of multivalued ρ-contractive-like, ρ-quasi-contractive-like, ρ-quasi-contractive, ρ-Zamfirescu and ρ-contraction mappings in the framework of modular function spaces. An example is presented to demonstrate the applicability of the implicit-type iterative schemes to the system of ordinary differential equations. Furthermore, numerical examples are given to show the rate of convergence of the various explicit Kirk-type and implicit Kirk-type iterative schemes under consideration. Our results complement the results obtained on normed and metric spaces in the literature. Also, our methods of proof serve as a guide to obtain several similar improved results for nonexpansive, pseudo-contractive, and accretive type mappings.

Keywords: implicit Kirk-type iterative schemes, multivalued mappings, convergence results, fixed point

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8239 An Efficient Separation for Convolutive Mixtures

Authors: Salah Al-Din I. Badran, Samad Ahmadi, Dylan Menzies, Ismail Shahin

Abstract:

This paper describes a new efficient blind source separation method; in this method we use a non-uniform filter bank and a new structure with different sub-bands. This method provides a reduced permutation and increased convergence speed comparing to the full-band algorithm. Recently, some structures have been suggested to deal with two problems: reducing permutation and increasing the speed of convergence of the adaptive algorithm for correlated input signals. The permutation problem is avoided with the use of adaptive filters of orders less than the full-band adaptive filter, which operate at a sampling rate lower than the sampling rate of the input signal. The decomposed signals by analysis bank filter are less correlated in each sub-band than the input signal at full-band, and can promote better rates of convergence.

Keywords: Blind source separation, estimates, full-band, mixtures, sub-band

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8238 Formation of Convergence Culture in the Framework of Conventional Media and New Media

Authors: Berkay Buluş, Aytekin İşman, Kübra Yüzüncüyıl

Abstract:

Developments in media and communication technologies have changed the way we use media. The importance of convergence culture has been increasing day by day within the framework of these developments. With new media, it is possible to say that social networks are the most powerful platforms that are integrated to this digitalization process. Although social networks seem like the place that people can socialize, they can also be utilized as places of production. On the other hand, audience has become users within the framework of transformation from national to global broadcasting. User generated contents make conventional media and new media collide. In this study, these communication platforms will be examined not as platforms that replace one another but mediums that unify each other. In the light of this information, information that is produced by users regarding new media platforms and all new media use practices are called convergence culture. In other words, convergence culture means intersections of conventional and new media. In this study, examples of convergence culture will be analyzed in detail.

Keywords: new media, convergence culture, convergence, use of new media, user generated content

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8237 Split Monotone Inclusion and Fixed Point Problems in Real Hilbert Spaces

Authors: Francis O. Nwawuru

Abstract:

The convergence analysis of split monotone inclusion problems and fixed point problems of certain nonlinear mappings are investigated in the setting of real Hilbert spaces. Inertial extrapolation term in the spirit of Polyak is incorporated to speed up the rate of convergence. Under standard assumptions, a strong convergence of the proposed algorithm is established without computing the resolvent operator or involving Yosida approximation method. The stepsize involved in the algorithm does not depend on the spectral radius of the linear operator. Furthermore, applications of the proposed algorithm in solving some related optimization problems are also considered. Our result complements and extends numerous results in the literature.

Keywords: fixedpoint, hilbertspace, monotonemapping, resolventoperators

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8236 A Transform Domain Function Controlled VSSLMS Algorithm for Sparse System Identification

Authors: Cemil Turan, Mohammad Shukri Salman

Abstract:

The convergence rate of the least-mean-square (LMS) algorithm deteriorates if the input signal to the filter is correlated. In a system identification problem, this convergence rate can be improved if the signal is white and/or if the system is sparse. We recently proposed a sparse transform domain LMS-type algorithm that uses a variable step-size for a sparse system identification. The proposed algorithm provided high performance even if the input signal is highly correlated. In this work, we investigate the performance of the proposed TD-LMS algorithm for a large number of filter tap which is also a critical issue for standard LMS algorithm. Additionally, the optimum value of the most important parameter is calculated for all experiments. Moreover, the convergence analysis of the proposed algorithm is provided. The performance of the proposed algorithm has been compared to different algorithms in a sparse system identification setting of different sparsity levels and different number of filter taps. Simulations have shown that the proposed algorithm has prominent performance compared to the other algorithms.

Keywords: adaptive filtering, sparse system identification, TD-LMS algorithm, VSSLMS algorithm

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8235 An Iterative Family for Solution of System of Nonlinear Equations

Authors: Sonia Sonia

Abstract:

This paper presents a family of iterative scheme for solving nonlinear systems of equations which have wide application in sciences and engineering. The proposed iterative family is based upon some parameters which generates many different iterative schemes. This family is completely derivative free and uses first of divided difference operator. Moreover some numerical experiments are performed and compared with existing methods. Analysis of convergence shows that the presented family has fourth-order of convergence. The dynamical behaviour of proposed family and local convergence have also been discussed. The numerical performance and convergence region comparison demonstrates that proposed family is efficient.

Keywords: convergence, divided difference operator, nonlinear system, Newton's method

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8234 A New Modification of Nonlinear Conjugate Gradient Coefficients with Global Convergence Properties

Authors: Ahmad Alhawarat, Mustafa Mamat, Mohd Rivaie, Ismail Mohd

Abstract:

Conjugate gradient method has been enormously used to solve large scale unconstrained optimization problems due to the number of iteration, memory, CPU time, and convergence property, in this paper we find a new class of nonlinear conjugate gradient coefficient with global convergence properties proved by exact line search. The numerical results for our new βK give a good result when it compared with well-known formulas.

Keywords: conjugate gradient method, conjugate gradient coefficient, global convergence

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8233 Comparison Analysis of Multi-Channel Echo Cancellation Using Adaptive Filters

Authors: Sahar Mobeen, Anam Rafique, Irum Baig

Abstract:

Acoustic echo cancellation in multichannel is a system identification application. In real time environment, signal changes very rapidly which required adaptive algorithms such as Least Mean Square (LMS), Leaky Least Mean Square (LLMS), Normalized Least Mean square (NLMS) and average (AFA) having high convergence rate and stable. LMS and NLMS are widely used adaptive algorithm due to less computational complexity and AFA used of its high convergence rate. This research is based on comparison of acoustic echo (generated in a room) cancellation thorough LMS, LLMS, NLMS, AFA and newly proposed average normalized leaky least mean square (ANLLMS) adaptive filters.

Keywords: LMS, LLMS, NLMS, AFA, ANLLMS

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8232 A Family of Distributions on Learnable Problems without Uniform Convergence

Authors: César Garza

Abstract:

In supervised binary classification and regression problems, it is well-known that learnability is equivalent to a uniform convergence of the hypothesis class, and if a problem is learnable, it is learnable by empirical risk minimization. For the general learning setting of unsupervised learning tasks, there are non-trivial learning problems where uniform convergence does not hold. We present here the task of learning centers of mass with an extra feature that “activates” some of the coordinates over the unit ball in a Hilbert space. We show that the learning problem is learnable under a stable RLM rule. We introduce a family of distributions over the domain space with some mild restrictions for which the sample complexity of uniform convergence for these problems must grow logarithmically with the dimension of the Hilbert space. If we take this dimension to infinity, we obtain a learnable problem for which the uniform convergence property fails for a vast family of distributions.

Keywords: statistical learning theory, learnability, uniform convergence, stability, regularized loss minimization

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8231 Semilocal Convergence of a Three Step Fifth Order Iterative Method under Hölder Continuity Condition in Banach Spaces

Authors: Ramandeep Behl, Prashanth Maroju, S. S. Motsa

Abstract:

In this paper, we study the semilocal convergence of a fifth order iterative method using recurrence relation under the assumption that first order Fréchet derivative satisfies the Hölder condition. Also, we calculate the R-order of convergence and provide some a priori error bounds. Based on this, we give existence and uniqueness region of the solution for a nonlinear Hammerstein integral equation of the second kind.

Keywords: Holder continuity condition, Frechet derivative, fifth order convergence, recurrence relations

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8230 Poster : Incident Signals Estimation Based on a Modified MCA Learning Algorithm

Authors: Rashid Ahmed , John N. Avaritsiotis

Abstract:

Many signal subspace-based approaches have already been proposed for determining the fixed Direction of Arrival (DOA) of plane waves impinging on an array of sensors. Two procedures for DOA estimation based neural networks are presented. First, Principal Component Analysis (PCA) is employed to extract the maximum eigenvalue and eigenvector from signal subspace to estimate DOA. Second, minor component analysis (MCA) is a statistical method of extracting the eigenvector associated with the smallest eigenvalue of the covariance matrix. In this paper, we will modify a Minor Component Analysis (MCA(R)) learning algorithm to enhance the convergence, where a convergence is essential for MCA algorithm towards practical applications. The learning rate parameter is also presented, which ensures fast convergence of the algorithm, because it has direct effect on the convergence of the weight vector and the error level is affected by this value. MCA is performed to determine the estimated DOA. Preliminary results will be furnished to illustrate the convergences results achieved.

Keywords: Direction of Arrival, neural networks, Principle Component Analysis, Minor Component Analysis

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8229 Maxwell’s Economic Demon Hypothesis and the Impossibility of Economic Convergence of Developing Economies

Authors: Firano Zakaria, Filali Adib Fatine

Abstract:

The issue f convergence in theoretical models (classical or Keynesian) has been widely discussed. The results of the work affirm that most countries are seeking to get as close as possible to a steady state in order to catch up with developed countries. In this paper, we have retested this question whether it is absolute or conditional. The results affirm that the degree of convergence of countries like Morocco is very low and income is still far from its equilibrium state. Moreover, the analysis of financial convergence, of the countries in our panel, states that the pace in this sector is more intense: countries are converging more rapidly in financial terms. The question arises as to why, with a fairly convergent financial system, growth does not respond, yet the financial system should facilitate this economic convergence. Our results confirm that the degree of information exchange between the financial system and the economic system did not change significantly between 1985 and 2017. This leads to the hypothesis that the financial system is failing to serve its role as a creator of information in developing countries despite all the reforms undertaken, thus making the existence of an economic demon in the Maxwell prevail.

Keywords: economic convergence, financial convergence, financial system, entropy

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8228 Modified Newton's Iterative Method for Solving System of Nonlinear Equations in Two Variables

Authors: Sara Mahesar, Saleem M. Chandio, Hira Soomro

Abstract:

Nonlinear system of equations in two variables is a system which contains variables of degree greater or equal to two or that comprises of the transcendental functions. Mathematical modeling of numerous physical problems occurs as a system of nonlinear equations. In applied and pure mathematics it is the main dispute to solve a system of nonlinear equations. Numerical techniques mainly used for finding the solution to problems where analytical methods are failed, which leads to the inexact solutions. To find the exact roots or solutions in case of the system of non-linear equations there does not exist any analytical technique. Various methods have been proposed to solve such systems with an improved rate of convergence and accuracy. In this paper, a new scheme is developed for solving system of non-linear equation in two variables. The iterative scheme proposed here is modified form of the conventional Newton’s Method (CN) whose order of convergence is two whereas the order of convergence of the devised technique is three. Furthermore, the detailed error and convergence analysis of the proposed method is also examined. Additionally, various numerical test problems are compared with the results of its counterpart conventional Newton’s Method (CN) which confirms the theoretic consequences of the proposed method.

Keywords: conventional Newton’s method, modified Newton’s method, order of convergence, system of nonlinear equations

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