Search results for: iterative process

Authors: Safeer Hussain Khan

Abstract:

In this paper, we prove a strong convergence result using a recently introduced iterative process with contractive-like operators. This improves and generalizes corresponding results in the literature in two ways: the iterative process is faster, operators are more general. In the end, we indicate that the results can also be proved with the iterative process with error terms.

Keywords: contractive-like operator, iterative process, fixed point, strong convergence

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Authors: Safeer Hussain Khan, H. Fukhar-ud-Din

Abstract:

The concept of quasi-contractive type operators was given by Berinde and extended by Imoru and Olatinwo. They named this new type as contractive-like operators. On the other hand, Xu and Noo introduced a three-step-one-mappings iterative process which can be seen as a generalization of Mann and Ishikawa iterative processes. Approximating common fixed points has its own importance as it has a direct link with minimization problem. Motivated by this, in this paper, we first extend the iterative process of Xu and Noor to the case of three-step-three-mappings and then prove a strong convergence result using contractive-like operators for this iterative process. In general, this generalizes corresponding results using Mann, Ishikawa and Xu-Noor iterative processes with quasi-contractive type operators. It is to be pointed out that our results can also be proved with iterative process involving error terms.

Keywords: contractive-like operator, iterative process, common fixed point, strong convergence

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Authors: Safeer Hussain Khan

Abstract:

In this paper, we introduce a two-step iterative algorithm to prove a strong convergence result for approximating common fixed points of three contractive-like operators. Our algorithm basically generalizes an existing algorithm..Our iterative algorithm also contains two famous iterative algorithms: Mann iterative algorithm and Ishikawa iterative algorithm. Thus our result generalizes the corresponding results proved for the above three iterative algorithms to a class of more general operators. At the end, we remark that nothing prevents us to extend our result to the case of the iterative algorithm with error terms.

Keywords: contractive-like operator, iterative algorithm, fixed point, strong convergence

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Authors: B. S. Akhmetov, S. T. Akhmetova, A. I. Ivanov, T. S. Kartbayev, A. Y. Malygin

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The problem of training of a network of artificial neurons in biometric appendices is that this process has to be completely automatic, i.e. the person operator should not participate in it. Therefore, this article discusses the issues of training the network of artificial neurons and the description of the non-iterative learning algorithm of artificial neuron.

Keywords: artificial neuron, biometrics, biometrical applications, learning of neuron, non-iterative algorithm

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Authors: Hwan-Jun Choi, Sung-Bok Choi, Hyoung-Kyu Song

Abstract:

Recently, among the MIMO-OFDM detection techniques, a lot of papers suggested V-BLAST scheme which can achieve high data rate. Therefore, the signal detection of MIMOOFDM system is important issue. In this paper, efficient iterative VBLAST detection technique is proposed in wireless communication system. The proposed scheme adjusts the number of candidate symbol and iterative scheme based on channel state. According to the simulation result, the proposed scheme has better BER performance than conventional schemes and similar BER performance of the QRD-M with iterative scheme. Moreover complexity of proposed scheme has 50.6 % less than complexity of QRD-M detection with iterative scheme. Therefore the proposed detection scheme can be efficiently used in wireless communication.

Keywords: MIMO-OFDM, V-BLAST, QR-decomposition, QRDM, DFE, iterative scheme, channel condition

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Authors: Thorsten Prante, Robert Schöch, Ruth Fleisch, Vaheh Khachatouri, Alexander Walch

Abstract:

The development of industrial plant control software is a complex and often very expensive task. One of the core problems is that a lot of the implementation and adaptation work can only be done after the plant hardware has been installed. In this paper, we present our approach to virtually developing and validating plant-level control software of production plants. This way, plant control software can be virtually commissioned before actual ramp-up of a plant, reducing actual commissioning costs and time. Technically, this is achieved by linking the actual plant-wide process control software (often called plant server) and an elaborate virtual plant model together to form an emulation system. Method-wise, we are suggesting a four-step iterative process with well-defined increments and time frame. Our work is based on practical experiences from planning to commissioning and start-up of several cut-to-size plants.

Keywords: iterative system design, virtual plant engineering, plant control software, simulation and emulation, virtual commissioning

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Authors: Hussain K. Chaiel

Abstract:

The development in the field of the digital signal processing (DSP) and the microelectronics technology reduces the complexity of the iterative algorithms that need large number of arithmetic operations. Virtex-Field Programmable Gate Arrays (FPGAs) are programmable silicon foundations which offer an important solution for addressing the needs of high performance DSP designer. In this work, Virtex-7 FPGA technology is used to implement an iterative algorithm to estimate the earthquake location. Simulation results show that an implementation based on block RAMB36E1 and DSP48E1 slices of Virtex-7 type reduces the number of cycles of the clock frequency. This enables the algorithm to be used for earthquake prediction.

Keywords: DSP, earthquake, FPGA, iterative algorithm

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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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Authors: Hudson Akewe

Abstract:

In this study, we introduce a modified Jungck (Dual Jungck) iterative scheme and use the scheme to approximate the unique common fixed point of a pair of generalized contractive-like operators in a Banach space. The iterative scheme is also shown to be stable with respect to the maps (S,T). An example is taken to justify the convergence of the scheme. Our result is a generalization and improvement of several results in the literature on single map T.

Keywords: generalized contractive-like operators, modified Jungck iterative scheme, stability results, weakly compatible maps, unique common fixed point

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Authors: Adarsh Shroff

Abstract:

Big data is a collection of dataset so large and complex that it becomes difficult to process using data base management tools. To perform operations like search, analysis, visualization on big data by using data mining; which is the process of extraction of patterns or knowledge from large data set. In recent years, the data mining applications become stale and obsolete over time. Incremental processing is a promising approach to refreshing mining results. It utilizes previously saved states to avoid the expense of re-computation from scratch. This project uses i2MapReduce, an incremental processing extension to Map Reduce, the most widely used framework for mining big data. I2MapReduce performs key-value pair level incremental processing rather than task level re-computation, supports not only one-step computation but also more sophisticated iterative computation, which is widely used in data mining applications, and incorporates a set of novel techniques to reduce I/O overhead for accessing preserved fine-grain computation states. To optimize the mining results, evaluate i2MapReduce using a one-step algorithm and three iterative algorithms with diverse computation characteristics for efficient mining.

Keywords: big data, map reduce, incremental processing, iterative computation

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Authors: Sari F. Alkhatib, Chang Je Park, Gyuhong Roh, Daeseong Jo

Abstract:

The iterative scheme which is used to treat buildup factors for stratified shields of three-layers or more is being investigated here using the layer-splitting technique. The second layer in a double-layer shield was split into two equivalent layers and the scheme was implemented on the new 'three-layer' shield configuration. The results of such manipulation for water-lead and water-iron shields combinations are presented here for 1 MeV photons. It was found that splitting the second layer introduces some deviation on the overall buildup factor. This expected deviation appeared to be higher in the case of low Z layer followed by high Z. However, the iterative scheme showed a great consistency and strong coherence with the introduced changes.

Keywords: build-up factor, iterative scheme, stratified shields, radiation protection

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Authors: Nadaniela Egidi, Pierluigi Maponi

Abstract:

The approximate solution of a time-harmonic electromagnetic scattering problem for inhomogeneous media is required in several application contexts, and its two-dimensional formulation is a Fredholm integral equation of the second kind. This integral equation provides a formulation for the direct scattering problem, but it has to be solved several times also in the numerical solution of the corresponding inverse scattering problem. The discretization of this Fredholm equation produces large and dense linear systems that are usually solved by iterative methods. In order to improve the efficiency of these iterative methods, we use the Symmetric SOR preconditioning, and we propose an algorithm for the evaluation of the associated relaxation parameter. We show the efficiency of the proposed algorithm by several numerical experiments, where we use two Krylov subspace methods, i.e., Bi-CGSTAB and GMRES.

Keywords: Fredholm integral equation, iterative method, preconditioning, scattering problem

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Authors: Sari F. Alkhatib, Chang Je Park, Gyuhong Roh

Abstract:

The iterative scheme which is used to treat buildup factors for stratified shields is being investigated here using the layer-splitting technique. A simple suggested formalism for the scheme based on the Kalos’ formula is introduced, based on which the implementation of the testing technique is carried out. The second layer in a double-layer shield was split into two equivalent layers and the scheme (with the suggested formalism) was implemented on the new “three-layer” shield configuration. The results of such manipulation on water-lead and water-iron shields combinations are presented here for 1 MeV photons. It was found that splitting the second layer introduces some deviation on the overall buildup factor value. This expected deviation appeared to be higher in the case of low Z layer followed by high Z. However, the overall performance of the iterative scheme showed a great consistency and strong coherence even with the introduced changes. The introduced layer-splitting testing technique shows the capability to be implemented in test the iterative scheme with a wide range of formalisms.

Keywords: buildup factor, iterative scheme, stratified shields, layer-splitting tecnique

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Authors: Ahmed Machmoum, Malika El Kyal

Abstract:

We consider iterative parallel multi-splitting method for differential algebraic equations. The main feature of the proposed idea is to use the asynchronous form. We prove that the multi-splitting technique can effectively accelerate the convergent performance of the iterative process. The main characteristic of an asynchronous mode is that the local algorithm not have to wait at predetermined messages to become available. We allow some processors to communicate more frequently than others, and we allow the communication delays tobe substantial and unpredictable. Note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: computer, multi-splitting methods, asynchronous mode, differential algebraic systems

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Authors: Sam Teek Ling, Norhashidah Hj. Mohd. Ali

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We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.

Keywords: explicit group iterative method, finite difference, fourth order compact, Poisson equation

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Authors: Naser Alajmi, Ali Alobaidly, Mubarak Alhajri, Salem Salamah, Muhammad Alsubaie

Abstract:

Iterative Learning Control (ILC) known to be a controlling tool to overcome periodic disturbances for repetitive systems. This technique is required to let the error signal tends to zero as the number of operation increases. The learning process that lies within this context is strongly dependent on the initial input which if selected properly tends to let the learning process be more effective compared to the case where a system starts from blind. ILC uses previous recorded execution data to update the following execution/trial input such that a reference trajectory is followed to a high accuracy. Error convergence in ILC is generally highly dependent on the input applied to a plant for trial $1$, thus a good choice of initial starting input signal would make learning faster and as a consequence the error tends to zero faster as well. In the work presented within, an upper limit based on the Singular Values Principle (SV) is derived for the initial input signal applied at trial $1$ such that the system follow the reference in less number of trials without responding aggressively or exceeding the working envelope where a system is required to move within in a robot arm, for example. Simulation results presented illustrate the theory introduced within this paper.

Keywords: initial input, iterative learning control, maximum input, singular values

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Authors: Malika Elkyal

Abstract:

We consider an iterative parallel multi-splitting method for differential algebraic equations. The main feature of the proposed idea is to use the asynchronous form. We prove that the multi-splitting technique can effectively accelerate the convergent performance of the iterative process. The main characteristic of an asynchronous mode is that the local algorithm does not have to wait at predetermined messages to become available. We allow some processors to communicate more frequently than others, and we allow the communication delays to be substantial and unpredictable. Accordingly, we note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: parallel methods, asynchronous mode, multisplitting, differential algebraic equations

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Authors: Thierno Diop, Michel Fortin, Jean Deteix

Abstract:

Since the precise formulation of the elastic part is irrelevant for the description of the algorithm, we shall consider a generic case. In practice, however, we will have to deal with a non linear material (for instance a Mooney-Rivlin model). We are interested in solving a finite element approximation of the problem, leading to large-scale non linear discrete problems and, after linearization, to large linear systems and ultimately to calculations needing iterative methods. This also implies that penalty method, and therefore augmented Lagrangian method, are to be banned because of their negative effect on the condition number of the underlying discrete systems and thus on the convergence of iterative methods. This is in rupture to the mainstream of methods for contact in which augmented Lagrangian is the principal tool. We shall first present the problem and its discretization; this will lead us to describe a general solution algorithm relying on a preconditioner for saddle-point problems which we shall describe in some detail as it is not entirely standard. We will propose an iterative approach for solving three-dimensional frictional contact problems between elastic bodies, including contact with a rigid body, contact between two or more bodies and also self-contact.

Keywords: frictional contact, three-dimensional, large-scale, iterative method

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Authors: Felix Damilola Ajibade, Opeyemi O. Enoch, Taiwo Paul Fajusigbe

Abstract:

This paper is centered on conducting an inquiry into the stability of the F* iterative algorithm to the fixed point of a strongly pseudo-contractive mapping in the framework of uniformly convex Banach spaces. To achieve the desired result, certain existing inequalities in convex Banach spaces were utilized, as well as the stability criteria of Harder and Hicks. Other necessary conditions for the stability of the F* algorithm on strong pseudo-contractive mapping were also obtained. Through a numerical approach, we prove that the F* iterative algorithm is H-stable for strongly pseudo-contractive mapping. Finally, the solution of the mixed-type Volterra-Fredholm functional non-linear integral equation is estimated using our results.

Keywords: stability, F* -iterative algorithm, pseudo-contractive mappings, uniformly convex Banach space, mixed-type Volterra-Fredholm integral equation

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Authors: Young Hee Geum

Abstract:

In this paper, we present the iterative method and determine the control parameters to converge cubically for solving nonlinear equations. In addition, we derive the asymptotic error constant.

Keywords: asymptotic error constant, iterative method, multiple root, root-finding, order of convergent

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Authors: Karim S. Hassan, Hisham M. Hamed, Yassmine A. Fahmy, Ahmed F. Shalash

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The mismatch between in-phase and quadrature signals in Orthogonal frequency division multiplexing (OFDM) systems, such as DVB-T2, results in a severe degradation in performance. Several general solutions have been proposed in the past, but these are largely computationally intensive, leading to complex implementations. In this paper, we propose a relatively simple iterative solution, which provides good results in relatively few iterations, using fixed precision arithmetic. An additional advantage is that complex digital blocks, such as dividers and square root, are not required. Thus, the proposed solution may be implemented in relatively simple hardware.

Keywords: OFDM, DVB-T2, I/Q imbalance, I/Q mismatch, iterative method, fixed point, reduced complexity

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Authors: Rupu Yang, Cong Toan Tran, Assaad Zoughaib

Abstract:

The work provides an iterative nonlinear programming method to synthesize a heat exchanger network by manipulating the trade-offs between the heat load of process heat exchangers (HEs) and utilities. We consider for the synthesis problem two cases, the first one without fixed cost for HEs, and the second one with fixed cost. For the no fixed cost problem, the nonlinear programming (NLP) model with all the potential HEs is optimized to obtain the global optimum. For the case with fixed cost, the NLP model is iterated through adding/removing HEs. The method was applied in five case studies and illustrated quite well effectiveness. Among which, the approach reaches the lowest TAC (2,904,026$/year) compared with the best record for the famous Aromatic plants problem. It also locates a slightly better design than records in literature for a 10 streams case without fixed cost with only 1/9 computational time. Moreover, compared to the traditional mixed-integer nonlinear programming approach, the iterative NLP method opens a possibility to consider constraints (such as controllability or dynamic performances) that require knowing the structure of the network to be calculated.

Keywords: heat exchanger network, synthesis, NLP, optimization

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Authors: Onur Onder, Celal Tanuca, Mahir Ozil, Halil Sen, Alkım Ozkan, Engin Ceylan, Ali Istek, Ozgur Saglam

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White balance adjustment of LCD TVs is an important procedure which has a direct influence on quality perception. Existing methods adjust RGB gain and offset values in different white levels during production. This paper suggests an iterative method in which the gamma is pre-adjusted during the design stage, and only 80% white is adjusted during production by modifying only RGB gain values (offset values are not modified). This method reduces the white balance adjustment time, contributing to the total efficiency of the production. Experiment shows that the adjustment results are well within requirements.

Keywords: color temperature, LCD panel deviation, LCD TV manufacturing, white balance

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Authors: Ahmed Amrani, Oussama Allali, Amira Ben Hamida, Felix Defrance, Stephanie Morland, Eva Pineau, Thomas Lacroix

Abstract:

The energy planning process is a very complex task that involves several stakeholders and requires the consideration of several local and global factors and constraints. In order to optimize and simplify this process, we propose a tool-based iterative approach applied to district heating planning. We build our tool with the collaboration of a French territory using actual district data and implementing the European incentives. We set up an iterative process including data visualization and analysis, identification and extraction of information related to the area concerned by the operation, design of sustainable planning scenarios leveraging local renewable and recoverable energy sources, and finally, the evaluation of scenarios. The last step is performed by a dynamic digital twin replica of the city. Territory’s energy experts confirm that the tool provides them with valuable support towards sustainable energy planning.

Keywords: climate change, data management, decision support, digital twin, district heating, energy planning, renewables, smart city

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Authors: Norhashidah Hj. Mohd Ali, Teng Wai Ping

Abstract:

In this paper, we present a high order group explicit method in solving the two dimensional Helmholtz equation. The presented method is derived from a nine-point fourth order finite difference approximation formula obtained from a 45-degree rotation of the standard grid which makes it possible for the construction of iterative procedure with reduced complexity. The developed method will be compared with the existing group iterative schemes available in literature in terms of computational time, iteration counts, and computational complexity. The comparative performances of the methods will be discussed and reported.

Keywords: explicit group method, finite difference, helmholtz equation, rotated grid, standard grid

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Authors: Mohammad Farid

Abstract:

In this paper, we introduce and study an explicit iterative method based on hybrid extragradient method to approximate a common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converge strongly to the common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, extension and generalization of the previously known results in this area.

Keywords: generalized mixed equilibrium problem, fixed-point problem, nonexpansive semigroup, variational inequality problem, iterative algorithms, hybrid extragradient method

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Authors: Hussaini Doko Ibrahim, Hamilton Cyprian Chinwenyi, Henrietta Nkem Ude

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In this paper, efforts were made to examine and compare the algorithmic iterative solutions of the conjugate gradient method as against other methods such as Gauss-Seidel and Jacobi approaches for solving systems of linear equations of the form Ax=b, where A is a real n×n symmetric and positive definite matrix. We performed algorithmic iterative steps and obtained analytical solutions of a typical 3×3 symmetric and positive definite matrix using the three methods described in this paper (Gauss-Seidel, Jacobi, and conjugate gradient methods), respectively. From the results obtained, we discovered that the conjugate gradient method converges faster to exact solutions in fewer iterative steps than the two other methods, which took many iterations, much time, and kept tending to the exact solutions.

Keywords: conjugate gradient, linear equations, symmetric and positive definite matrix, gauss-seidel, Jacobi, algorithm

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Authors: Vikram Saini, Lillie Dewan

Abstract:

This paper presents the iterative schemes based on Least square, Hierarchical Least Square and Stochastic Approximation Gradient method for the Identification of Wiener model with parametric structure. A gradient method is presented for the parameter estimation of wiener model with noise conditions based on the stochastic approximation. Simulation results are presented for the Wiener model structure with different static non-linear elements in the presence of colored noise to show the comparative analysis of the iterative methods. The stochastic gradient method shows improvement in the estimation performance and provides fast convergence of the parameters estimates.

Keywords: hard non-linearity, least square, parameter estimation, stochastic approximation gradient, Wiener model

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Authors: N. Noroozian, M. Halim, B. Holloway

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Computed Tomography (CT) has become the largest source of radiation exposure in modern countries however, recent technological advances have created new methods to reduce dose without negatively affecting image quality. SAFIRE has emerged as a new software package which utilizes full raw data projections for iterative reconstruction, thereby allowing for lower CT dose to be used. this audit was performed to compare CT doses in certain examinations before and after the introduction of SAFIRE at our Radiology department which showed CT doses were significantly lower using SAFIRE compared with pre-SAFIRE software at SAFIRE 3 setting for the following studies:CSKUH Unenhanced brain scans (-20.9%), CABPEC Abdomen and pelvis with contrast (-21.5%), CCHAPC Chest with contrast (-24.4%), CCHAPC Abdomen and pelvis with contrast (-16.1%), CCHAPC Total chest, abdomen and pelvis (-18.7%).

Keywords: dose reduction, iterative reconstruction, low dose CT techniques, SAFIRE

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Authors: Lourenço Bastos, Filipa Carneiro, Bruno Vale, Rita Marques Joana Silva, Ricardo Freitas, Ângelo Marques, Sara Cortez, Alberta Coelho, Pedro Parreira, Liliana Sousa, Anabela Salgueiro, Bruno Silva

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The process of flushing is considered to be an adequate technique to reduce the risk of infection during the clinical practice of venous catheterization. Nonetheless, there is still a lack of adhesion to this method, in part due to the complexity of this procedure. The project SeringaDuo aimed to develop an innovative double-chamber syringe for intravenous sequential administration of drugs and serums. This device served the purpose of improving the adherence to the practice, through the reduction of manipulations needed, which also improves patient safety, and though the promotion of flushing practice by health professionals, by simplifying this task. To assist on the development of this innovative syringe, a numerical methodology was developed and validated in order to predict the syringe’s mechanical and flow behavior during the fluids’ loading and administration phases, as well as to allow the material behavior evaluation during its production. For this, three commercial numerical simulation software was used, namely ABAQUS, ANSYS/FLUENT, and MOLDFLOW. This methodology aimed to evaluate the concepts feasibility and to optimize the geometries of the syringe’s components, creating this way an iterative process for product development based on numerical simulations, validated by the production of prototypes. Through this methodology, it was possible to achieve a final design that fulfils all the characteristics and specifications defined. This iterative process based on numerical simulations is a powerful tool for product development that allows obtaining fast and accurate results without the strict need for prototypes. An iterative process can be implemented, consisting of consecutive constructions and evaluations of new concepts, to obtain an optimized solution, which fulfils all the predefined specifications and requirements.

Keywords: Venous catheterization, flushing, syringe, numerical simulation

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