Search results for: minimum norm

Authors: Minghui Wang, Luping Xu, Juntao Zhang

Abstract:

In this paper, according to the classical algorithm LSQR for solving the least-squares problem, an iterative method is proposed for least-squares solution of constrained matrix equation. By using the Kronecker product, the matrix-form LSQR is presented to obtain the like-minimum norm and minimum norm solutions in a constrained matrix set for the symmetric arrowhead matrices. Finally, numerical examples are also given to investigate the performance.

Keywords: Symmetric arrowhead matrix, iterative method, like-minimum norm, minimum norm, Algorithm LSQR.

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Authors: Minghui Wang

Abstract:

Based on the classical algorithm LSQR for solving (unconstrained) LS problem, an iterative method is proposed for the least-squares like-minimum-norm symmetric solution of AXB+CYD=E. As the application of this algorithm, an iterative method for the least-squares like-minimum-norm biymmetric solution of AXB=E is also obtained. Numerical results are reported that show the efficiency of the proposed methods.

Keywords: Matrix equation, bisymmetric matrix, least squares problem, like-minimum norm, iterative algorithm.

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Authors: Abdussamad U. Jibia, Momoh-Jimoh E. Salami

Abstract:

Eigenvector methods are gaining increasing acceptance in the area of spectrum estimation. This paper presents a successful attempt at testing and evaluating the performance of two of the most popular types of subspace techniques in determining the parameters of multiexponential signals with real decay constants buried in noise. In particular, MUSIC (Multiple Signal Classification) and minimum-norm techniques are examined. It is shown that these methods perform almost equally well on multiexponential signals with MUSIC displaying better defined peaks.

Keywords: Eigenvector, minimum norm, multiexponential, subspace.

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Authors: Jiashang Jiang, Hao Liu, Yongxin Yuan

Abstract:

In this paper the gradient based iterative algorithms are presented to solve the following four types linear matrix equations: (a) AXB = F; (b) AXB = F, CXD = G; (c) AXB = F s. t. X = XT ; (d) AXB+CYD = F, where X and Y are unknown matrices, A,B,C,D, F,G are the given constant matrices. It is proved that if the equation considered has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. The numerical results show that the proposed method is reliable and attractive.

Keywords: Matrix equation, iterative algorithm, parameter estimation, minimum norm solution.

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Authors: Yongxin Yuan, Jiashang Jiang

Abstract:

In this paper the gradient based iterative algorithm is presented to solve the linear matrix equation AXB +CXTD = E, where X is unknown matrix, A,B,C,D,E are the given constant matrices. It is proved that if the equation has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. Two numerical examples show that the introduced iterative algorithm is quite efficient.

Keywords: matrix equation, iterative algorithm, parameter estimation, minimum norm solution.

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Authors: Young-Seok Choi

Abstract:

We present a new subband adaptive filter (R-SAF) which is robust against impulsive noise in system identification. To address the vulnerability of adaptive filters based on the L2-norm optimization criterion against impulsive noise, the R-SAF comes from the L1-norm optimization criterion with a constraint on the energy of the weight update. Minimizing L1-norm of the a posteriori error in each subband with a constraint on minimum disturbance gives rise to the robustness against the impulsive noise and the capable convergence performance. Experimental results clearly demonstrate that the proposed R-SAF outperforms the classical adaptive filtering algorithms when impulsive noise as well as background noise exist.

Keywords: Subband adaptive filter, L1-norm, system identification, robustness, impulsive interference.

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Authors: Young-Seok Choi

Abstract:

This paper presents a normalized subband adaptive filtering (NSAF) algorithm to cope with the sparsity condition of an underlying system in the context of compressive sensing. By regularizing a weighted l1-norm of the filter taps estimate onto the cost function of the NSAF and utilizing a subgradient analysis, the update recursion of the l1-norm constraint NSAF is derived. Considering two distinct weighted l1-norm regularization cases, two versions of the l1-norm constraint NSAF are presented. Simulation results clearly indicate the superior performance of the proposed l1-norm constraint NSAFs comparing with the classical NSAF.

Keywords: Subband adaptive filtering, sparsity constraint, weighted l1-norm.

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Authors: C. S. Sastry, Saurabh Jain, Ashish Mishra

Abstract:

Image retrieval is a topic where scientific interest is currently high. The important steps associated with image retrieval system are the extraction of discriminative features and a feasible similarity metric for retrieving the database images that are similar in content with the search image. Gabor filtering is a widely adopted technique for feature extraction from the texture images. The recently proposed sparsity promoting l1-norm minimization technique finds the sparsest solution of an under-determined system of linear equations. In the present paper, the l1-norm minimization technique as a similarity metric is used in image retrieval. It is demonstrated through simulation results that the l1-norm minimization technique provides a promising alternative to existing similarity metrics. In particular, the cases where the l1-norm minimization technique works better than the Euclidean distance metric are singled out.

Keywords: l1-norm minimization, content based retrieval, modified Gabor function.

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Authors: Young-Seok Choi

Abstract:

This paper presents a subband adaptive filter (SAF) for a system identification where an impulse response is sparse and disturbed with an impulsive noise. Benefiting from the uses of l1-norm optimization and l0-norm penalty of the weight vector in the cost function, the proposed l0-norm sign SAF (l0-SSAF) achieves both robustness against impulsive noise and much improved convergence behavior than the classical adaptive filters. Simulation results in the system identification scenario confirm that the proposed l0-norm SSAF is not only more robust but also faster and more accurate than its counterparts in the sparse system identification in the presence of impulsive noise.

Keywords: Subband adaptive filter, l0-norm, sparse system, robustness, impulsive interference.

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Authors: Kui Du

Abstract:

Recently, Uhlig [Numer. Algorithms, 52(3):335-353, 2009] proposed open questions about the ratios between the spectral norm, the numerical radius and the spectral radius of a square matrix. In this note, we provide some observations to answer these questions.

Keywords: Spectral norm, Numerical radius, Spectral radius, Ratios

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Authors: Hyun-Chool Shin

Abstract:

In this paper we propose a simple adaptive algorithm iteratively solving the unit-norm constrained optimization problem. Instead of conventional parameter norm based normalization, the proposed algorithm incorporates scalar normalization which is computationally much simpler. The analysis of stationary point is presented to show that the proposed algorithm indeed solves the constrained optimization problem. The simulation results illustrate that the proposed algorithm performs as good as conventional ones while being computationally simpler.

Keywords: constrained optimization, unit-norm, LMS, principle component analysis.

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Authors: Yongxin Yuan

Abstract:

The problem of updating damped gyroscopic systems using measured modal data can be mathematically formulated as following two problems. Problem I: Given Ma ∈ Rn×n, Λ = diag{λ1, ··· , λp} ∈ Cp×p, X = [x1, ··· , xp] ∈ Cn×p, where p<n and both Λ and X are closed under complex conjugation in the sense that λ2j = λ¯2j−1 ∈ C, x2j = ¯x2j−1 ∈ Cn for j = 1, ··· , l, and λk ∈ R, xk ∈ Rn for k = 2l + 1, ··· , p, find real-valued symmetric matrices D,K and a real-valued skew-symmetric matrix G (that is, GT = −G) such that MaXΛ2 + (D + G)XΛ + KX = 0. Problem II: Given real-valued symmetric matrices Da, Ka ∈ Rn×n and a real-valued skew-symmetric matrix Ga, find (D, ˆ G, ˆ Kˆ ) ∈ SE such that Dˆ −Da2+Gˆ−Ga2+Kˆ −Ka2 = min(D,G,K)∈SE (D− Da2 + G − Ga2 + K − Ka2), where SE is the solution set of Problem I and · is the Frobenius norm. This paper presents an iterative algorithm to solve Problem I and Problem II. By using the proposed iterative method, a solution of Problem I can be obtained within finite iteration steps in the absence of roundoff errors, and the minimum Frobenius norm solution of Problem I can be obtained by choosing a special kind of initial matrices. Moreover, the optimal approximation solution (D, ˆ G, ˆ Kˆ ) of Problem II can be obtained by finding the minimum Frobenius norm solution of a changed Problem I. A numerical example shows that the introduced iterative algorithm is quite efficient.

Keywords: Model updating, iterative algorithm, gyroscopic system, partially prescribed spectral data, optimal approximation.

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Authors: V. Tawiwat, P. Jumnong

Abstract:

Both the minimum energy consumption and smoothness, which is quantified as a function of jerk, are generally needed in many dynamic systems such as the automobile and the pick-and-place robot manipulator that handles fragile equipments. Nevertheless, many researchers come up with either solely concerning on the minimum energy consumption or minimum jerk trajectory. This research paper proposes a simple yet very interesting when combining the minimum energy and jerk of indirect jerks approaches in designing the time-dependent system yielding an alternative optimal solution. Extremal solutions for the cost functions of the minimum energy, the minimum jerk and combining them together are found using the dynamic optimization methods together with the numerical approximation. This is to allow us to simulate and compare visually and statistically the time history of state inputs employed by combining minimum energy and jerk designs. The numerical solution of minimum direct jerk and energy problem are exactly the same solution; however, the solutions from problem of minimum energy yield the similar solution especially in term of tendency.

Keywords: Optimization, Dynamic, Linear Systems, Jerks.

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Authors: G. Sonfack, J. Mbihi, B. Lonla Moffo

Abstract:

This paper presents an optimal duty-cycle modulation (ODCM) scheme for analog-to-digital conversion (ADC) systems. The overall ODCM-Based ADC problem is decoupled into optimal DCM and digital filtering sub-problems, while taking into account constraints of mutual design parameters between the two. Using a set of three lemmas and four morphological theorems, the ODCM sub-problem is modelled as a nonlinear cost function with nonlinear constraints. Then, a weighted least p^th norm of the error between ideal and predicted frequency responses is used as a cost function for the digital filtering sub-problem. In addition, MATLAB fmincon and MATLAB iirlnorm tools are used as optimal DCM and least p^th norm solvers respectively. Furthermore, the virtual simulation scheme of an overall prototyping ODCM-based ADC system is implemented and well tested with the help of Simulink tool according to relevant set of design data, i.e., 3 KHz of modulating bandwidth, 172 KHz of maximum modulation frequency and 25 MHZ of sampling frequency. Finally, the results obtained and presented show that the ODCM-based ADC achieves under 3 KHz of modulating bandwidth: 57 dBc of SINAD (signal-to-noise and distorsion), 58 dB of SFDR (Surpious free dynamic range) -80 dBc of THD (total harmonic distorsion), and 10 bits of minimum resolution. These performance levels appear to be a great challenge within the class of oversampling ADC topologies, with 2^nd order IIR (infinite impulse response) decimation filter.

Keywords: Digital IIR filter, morphological lemmas and theorems, optimal DCM-based DAC, virtual simulation, weighted least pth norm.

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Authors: M. M. M. Jaradat, M. K. Al-Qeyyam

Abstract:

The length of a cycle basis of a graph is the sum of the lengths of its elements. A minimum cycle basis is a cycle basis with minimum length. In this work, a construction of a minimum cycle basis for the wreath product of wheels with stars is presented. Moreover, the length of minimum cycle basis and the length of its longest cycle are calculated.

Keywords: Cycle space, minimum cycle basis, wreath product.

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Authors: Samsudin A. Rahim, Latiffah Pawanteh, Ali Salman

Abstract:

This paper explores the changing trend in citizenship norms among young citizens from various ethnic groups in Malaysia and the extent to which it influences the participation of young citizens in political and civil issues. Embedded in democratic constitutions are the rights and freedoms that accompany citizenship, and these rights and freedoms include participation. Participation in democracies should go beyond voting; it should include taking part in the governance process. The political process is not at risk even though politics does not work as it did in the past. A national sample of 1697 respondents between the ages of 21 and 40 years were interviewed in January 2011. The findings show that respondents embrace an engaged-citizenship norm more than they do the traditional duty-citizen norm. Among the ethnic groups, the Chinese show lower means in both citizenship norms compared with other ethnic groups, namely, the Malays and the Indians. The duty-citizen norm correlates higher with political participation than with civic participation. On the other hand, the engaged-citizen norm correlates higher with civic participation than with political participation.

Keywords: citizenship norms, political participation, civic participation, youths, globalization

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Authors: Tawiwat V., Phermsak S., Noppasit C.

Abstract:

This paper deals with under actuator dynamic systems such as spring-mass-damper system when the number of control variable is less than the number of state variable. In order to apply optimal control, the controllability must be checked. There are many objective functions to be selected as the goal of the optimal control such as minimum energy, maximum energy and minimum jerk. As the objective function is the first priority, if one like to have the second goal to be applied; however, it could not fit in the objective function format and also avoiding the vector cost for the objective, this paper will illustrate the problem of under actuator dynamic systems with the easiest to deal with comparing between minimum energy and minimum jerk.

Keywords: Under actuator, Dynamic optimal control, Minimumjerk, Minimum energy.

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Authors: Tawiwat Veeraklaew, Nathasit Phathana-im, Songkit Heama

Abstract:

Both the minimum energy consumption and smoothness, which is quantified as a function of jerk, are generally needed in many dynamic systems such as the automobile and the pick-and-place robot manipulator that handles fragile equipments. Nevertheless, many researchers come up with either solely concerning on the minimum energy consumption or minimum jerk trajectory. This research paper proposes a simple yet very interesting relationship between the minimum direct and indirect jerks approaches in designing the time-dependent system yielding an alternative optimal solution. Extremal solutions for the cost functions of direct and indirect jerks are found using the dynamic optimization methods together with the numerical approximation. This is to allow us to simulate and compare visually and statistically the time history of control inputs employed by minimum direct and indirect jerk designs. By considering minimum indirect jerk problem, the numerical solution becomes much easier and yields to the similar results as minimum direct jerk problem.

Keywords: Optimization, Dynamic, Linear Systems, Jerks.

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Authors: S. Balaji, V. Swaminathan, K. Kannan

Abstract:

The Minimum Weighted Vertex Cover (MWVC) problem is a classic graph optimization NP - complete problem. Given an undirected graph G = (V, E) and weighting function defined on the vertex set, the minimum weighted vertex cover problem is to find a vertex set S V whose total weight is minimum subject to every edge of G has at least one end point in S. In this paper an effective algorithm, called Support Ratio Algorithm (SRA), is designed to find the minimum weighted vertex cover of a graph. Computational experiments are designed and conducted to study the performance of our proposed algorithm. Extensive simulation results show that the SRA can yield better solutions than other existing algorithms found in the literature for solving the minimum vertex cover problem.

Keywords: Weighted vertex cover, vertex support, approximation algorithms, NP-complete problem.

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Authors: V. Tereshchenko, A. Tregubenko

Abstract:

In this study we survey the method for fast finding a minimum link path between two arbitrary points within a simple polygon, which can pass only through the vertices, with preprocessing.

Keywords: Minimum link path, simple polygon, Steiner points, optimal algorithm.

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Authors: Young-Seok Choi

Abstract:

This work presents a new type of the affine projection (AP) algorithms which incorporate the sparsity condition of a system. To exploit the sparsity of the system, a weighted l1-norm regularization is imposed on the cost function of the AP algorithm. Minimizing the cost function with a subgradient calculus and choosing two distinct weighting for l1-norm, two stochastic gradient based sparsity regularized AP (SR-AP) algorithms are developed. Experimental results exhibit that the SR-AP algorithms outperform the typical AP counterparts for identifying sparse systems.

Keywords: System identification, adaptive filter, affine projection, sparsity, sparse system.

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Authors: Jiashang Jiang

Abstract:

Model updating is an inverse eigenvalue problem which concerns the modification of an existing but inaccurate model with measured modal data. In this paper, an efficient gradient based iterative method for updating the mass, damping and stiffness matrices simultaneously using a few of complex measured modal data is developed. Convergence analysis indicates that the iterative solutions always converge to the unique minimum Frobenius norm symmetric solution of the model updating problem by choosing a special kind of initial matrices.

Keywords: Model updating, iterative algorithm, damped structural system, optimal approximation.

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Authors: Tawiwat V., Narongkorn D., Auttapoom L.

Abstract:

This research proposes the change of damping coefficient regarding minimum displacement. From the mass with external forced and damper problem, when is the constant external forced transmitted to the understructure in the difference angle between 30 and 60 degrees. This force generates the vibration as general known; however, the objective of this problem is to have minimum displacement. As the angle is changed and the goal is the same; therefore, the damper of the system must be varied while keeping constant spring stiffness. The problem is solved by using nonlinear programming and the suitable changing of the damping coefficient is provided.

Keywords: Damping coefficient, Optimal control, Minimum Displacement and Vibration

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Authors: Luke McDonagh

Abstract:

Over the past three decades, free and open source software (FOSS) programmers have developed new, innovative and legally binding licences that have in turn enabled the creation of innumerable pieces of everyday software, including Linux, Mozilla Firefox and Open Office. That FOSS has been highly successful in competing with 'closed source software' (e.g. Microsoft Office) is now undeniable, but in noting this success, it is important to examine in detail why this system of FOSS has been so successful. One key reason is the existence of networks or communities of programmers, who are bound together by a key shared social norm of 'reciprocity'. At the same time, these FOSS networks are not unitary – they are highly diverse and there are large divergences of opinion between members regarding which licences are generally preferable: some members favour the flexible ‘free’ or 'no copyleft' licences, such as BSD and MIT, while other members favour the ‘strong open’ or 'strong copyleft' licences such as GPL. This paper argues that without both the existence of the shared norm of reciprocity and the diversity of licences, it is unlikely that the innovative legal framework provided by FOSS would have succeeded to the extent that it has.

Keywords: Open source, software, licences, reciprocity, networks.

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Authors: Abida Harbi

Abstract:

We provide a maximum norm analysis of a finite element Schwarz alternating method for a nonlinear elliptic boundary value problem of the form -Δu = f(u), on two overlapping sub domains with non matching grids. We consider a domain which is the union of two overlapping sub domains where each sub domain has its own independently generated grid. The two meshes being mutually independent on the overlap region, a triangle belonging to one triangulation does not necessarily belong to the other one. Under a Lipschitz assumption on the nonlinearity, we establish, on each sub domain, an optimal L∞ error estimate between the discrete Schwarz sequence and the exact solution of the boundary value problem.

Keywords: Error estimates, Finite elements, Nonlinear PDEs, Schwarz method.

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Authors: Nazaket Gazieva

Abstract:

Voice biometric data associated with physiological, psychological and other factors are widely used in forensic phonoscopy. There are various methods for identifying and verifying a person by voice. This article explores the minimum speech signal data as individual parameters of a speech signal. Monozygotic twins are believed to be genetically identical. Using the minimum data of the speech signal, we came to the conclusion that the voice imprint of monozygotic twins is individual. According to the conclusion of the experiment, we can conclude that the minimum indicators of the speech signal are more stable and reliable for phonoscopic examinations.

Keywords: Biometric voice prints, fundamental frequency, phonogram, speech signal, temporal characteristics.

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Authors: Marzieh Dosti, Alireza Nazemi

Abstract:

Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this paper, a numerical solution for the one-dimensional hyperbolic telegraph equation by using the collocation method using the septic splines is proposed. The scheme works in a similar fashion as finite difference methods. Test problems are used to validate our scheme by calculate L2-norm and L∞-norm. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found to be in good agreement with the exact solutions.

Keywords: B-spline, collocation method, second-order hyperbolic telegraph equation, difference schemes.

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Authors: Francisco José Plácido da Cunha, Tassio Ferenzini Martins Sirqueira, Marx Leles Viana, Carlos José Pereira de Lucena

Abstract:

Open Multiagent Systems (MASs) are societies in which heterogeneous and independently designed entities (agents) work towards similar, or different ends. Software agents are autonomous and the diversity of interests among different members living in the same society is a fact. In order to deal with this autonomy, these open systems use mechanisms of social control (norms) to ensure a desirable social order. This paper considers the following types of norms: (i) obligation — agents must accomplish a specific outcome; (ii) permission — agents may act in a particular way, and (iii) prohibition — agents must not act in a specific way. All of these characteristics mean to encourage the fulfillment of norms through rewards and to discourage norm violation by pointing out the punishments. Once the software agent decides that its priority is the satisfaction of its own desires and goals, each agent must evaluate the effects associated to the fulfillment of one or more norms before choosing which one should be fulfilled. The same applies when agents decide to violate a norm. This paper also introduces a framework for the development of MASs that provide support mechanisms to the agent’s decision-making, using norm-based reasoning. The applicability and validation of this approach is demonstrated applying a traffic intersection scenario.

Keywords: BDI aAgent, BDI4JADE framework, multiagent system, normative agents.

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Authors: Qamar Saeed, Vali Uddin, Reza Katebi

Abstract:

In this paper multivariable predictive PID controller has been implemented on a multi-inputs multi-outputs control problem i.e., quadruple tank system, in comparison with a simple multiloop PI controller. One of the salient feature of this system is an adjustable transmission zero which can be adjust to operate in both minimum and non-minimum phase configuration, through the flow distribution to upper and lower tanks in quadruple tank system. Stability and performance analysis has also been carried out for this highly interactive two input two output system, both in minimum and non-minimum phases. Simulations of control system revealed that better performance are obtained in predictive PID design.

Keywords: Proportional-integral-derivative Control, GeneralizedPredictive Control, Predictive PID Control, Multivariable Systems

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Authors: Leehter Yao, Kuei-Song Weng, Cherng-Dir Huang

Abstract:

A fuzzy classifier using multiple ellipsoids approximating decision regions for classification is to be designed in this paper. An algorithm called Gustafson-Kessel algorithm (GKA) with an adaptive distance norm based on covariance matrices of prototype data points is adopted to learn the ellipsoids. GKA is able toadapt the distance norm to the underlying distribution of the prototypedata points except that the sizes of ellipsoids need to be determined a priori. To overcome GKA's inability to determine appropriate size ofellipsoid, the genetic algorithm (GA) is applied to learn the size ofellipsoid. With GA combined with GKA, it will be shown in this paper that the proposed method outperforms the benchmark algorithms as well as algorithms in the field.

Keywords: Ellipsoids, genetic algorithm, classification, fuzzyc-means (FCM)

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