scholarly journals On the strong P-regular splitting iterative methods for non-Hermitian linear systems

2021 ◽  
Vol 6 (11) ◽  
pp. 11879-11893
Author(s):  
Junxiang Lu ◽  
◽  
Chengyi Zhang ◽  
Keyword(s):  
Linear Systems ◽  
Iterative Methods ◽  
Numerical Experiments ◽  
Regular Splitting

<abstract><p>The strong <italic>P</italic>-regular splitting is put forward and defined for iterative methods of non-Hermitian linear systems in the paper. The strong <italic>P</italic>-regular splitting combining SOR iterative methods and relaxed SOR iterative methods are established, and conditions guaranteeing the convergence are presented. Furthermore, two numerical experiments are done to illustrate the convergence and effectiveness of our iterative methods.</p></abstract>

Modified Iterative Methods for Solving Fully Fuzzy Linear Systems

Fuzzy Systems ◽  
2017 ◽  
pp. 55-73
Author(s):  
S. A. Edalatpanah
Keyword(s):  
Linear Systems ◽  
Iterative Methods ◽  
Fuzzy System ◽  
Numerical Experiments ◽  
Linear Equations ◽  
Numerical Procedure ◽  
Numerical Results ◽  
System Of Linear Equations ◽  
Iterative Schemes ◽  
Fuzzy Linear Systems

In the present chapter, we give an overview of computational iterative schemes for fuzzy system of linear equations. We also consider fully fuzzy linear systems (FFLS) and demonstrate a class of the existing iterative methods using the splitting approach for calculating the solution. Furthermore, the main aim in this work is to design a numerical procedure for improving this algorithm. Some numerical experiments are illustrated to show the applicability of the methods and to show the efficiency of proposed algorithm, we report the numerical results of large-scaled fuzzy problems.

scholarly journals Convergent Homotopy Analysis Method for Solving Linear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
H. Nasabzadeh ◽  
F. Toutounian
Keyword(s):  
Iterative Method ◽  
Linear Systems ◽  
Iterative Methods ◽  
Homotopy Analysis Method ◽  
Numerical Experiments ◽  
Series Solution ◽  
Iterative Scheme ◽  
New Method ◽  
Analysis Method ◽  
Homotopy Analysis

By using homotopy analysis method (HAM), we introduce an iterative method for solving linear systems. This method (HAM) can be used to accelerate the convergence of the basic iterative methods. We also show that by applying HAM to a divergent iterative scheme, it is possible to construct a convergent homotopy-series solution when the iteration matrix G of the iterative scheme has particular properties such as being symmetric, having real eigenvalues. Numerical experiments are given to show the efficiency of the new method.

Modified Iterative Methods for Solving Fully Fuzzy Linear Systems

2017 ◽  
pp. 322-339
Author(s):  
S. A. Edalatpanah
Keyword(s):  
Linear Systems ◽  
Iterative Methods ◽  
Fuzzy System ◽  
Numerical Experiments ◽  
Linear Equations ◽  
Numerical Procedure ◽  
Numerical Results ◽  
System Of Linear Equations ◽  
Iterative Schemes ◽  
Fuzzy Linear Systems

In the present chapter, we give an overview of computational iterative schemes for fuzzy system of linear equations. We also consider fully fuzzy linear systems (FFLS) and demonstrate a class of the existing iterative methods using the splitting approach for calculating the solution. Furthermore, the main aim in this work is to design a numerical procedure for improving this algorithm. Some numerical experiments are illustrated to show the applicability of the methods and to show the efficiency of proposed algorithm, we report the numerical results of large-scaled fuzzy problems.

scholarly journals Analysis of Some Nonstationary Iterative Methods Using the Pascal and Vandermonde Linear Systems

2021 ◽  
pp. 1-3
Author(s):  
Azizu S ◽  
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Iterative Methods ◽  
Programming Language ◽  
Numerical Experiments ◽  
Polynomial Function ◽  
Paper Analysis ◽  
Vandermonde Matrix ◽  
Cubic Polynomial ◽  
Matlab Programming

In this paper, analysis of some nonstationary iterative methods using the Vandermonde and Pascal linear system is reported. The nonstationary iterative methods selected were GMRES and QMR to assess their performance on the identified linear systems. The paper focused on the convergence relative residual and number of iteration for each type of chosen linear system. The Vandermonde matrix is mostly applied to interpolation of both quadratic and cubic polynomial function. The resulting polynomial has the form: p(x) = an xn + an-1xn-1 +...+ a1 x + a0 . From the numerical experiments conducted using the matlab programming language, the GMRES is recommended when solving the identified linear systems

scholarly journals Multipreconditioned GMRES for simulating stochastic automata networks

2018 ◽  
Vol 16 (1) ◽  
pp. 986-998
Author(s):  
Chun Wen ◽  
Ting-Zhu Huang ◽  
Xian-Ming Gu ◽  
Zhao-Li Shen ◽  
Hong-Fan Zhang ◽  
...  
Keyword(s):  
Steady State ◽  
Probability Distribution ◽  
Linear Systems ◽  
Iterative Methods ◽  
Communication Systems ◽  
Queueing Systems ◽  
Steady State Probability ◽  
Stochastic Automata ◽  
Automata Networks ◽  
Generator Matrices

AbstractStochastic Automata Networks (SANs) have a large amount of applications in modelling queueing systems and communication systems. To find the steady state probability distribution of the SANs, it often needs to solve linear systems which involve their generator matrices. However, some classical iterative methods such as the Jacobi and the Gauss-Seidel are inefficient due to the huge size of the generator matrices. In this paper, the multipreconditioned GMRES (MPGMRES) is considered by using two or more preconditioners simultaneously. Meanwhile, a selective version of the MPGMRES is presented to overcome the rapid increase of the storage requirements and make it practical. Numerical results on two models of SANs are reported to illustrate the effectiveness of these proposed methods.

scholarly journals Amesos2 and Belos: Direct and Iterative Solvers for Large Sparse Linear Systems

2012 ◽  
Vol 20 (3) ◽  
pp. 241-255 ◽  
Author(s):  
Eric Bavier ◽  
Mark Hoemmen ◽  
Sivasankaran Rajamanickam ◽  
Heidi Thornquist
Keyword(s):  
Linear Systems ◽  
Iterative Methods ◽  
Sparse Matrix ◽  
Sparse Matrices ◽  
Direct Methods ◽  
Iterative Solvers ◽  
Software Project ◽  
Sparse Linear Systems ◽  
Scalar Type ◽  
Mixed Precision

Solvers for large sparse linear systems come in two categories: direct and iterative. Amesos2, a package in the Trilinos software project, provides direct methods, and Belos, another Trilinos package, provides iterative methods. Amesos2 offers a common interface to many different sparse matrix factorization codes, and can handle any implementation of sparse matrices and vectors, via an easy-to-extend C++ traits interface. It can also factor matrices whose entries have arbitrary “Scalar” type, enabling extended-precision and mixed-precision algorithms. Belos includes many different iterative methods for solving large sparse linear systems and least-squares problems. Unlike competing iterative solver libraries, Belos completely decouples the algorithms from the implementations of the underlying linear algebra objects. This lets Belos exploit the latest hardware without changes to the code. Belos favors algorithms that solve higher-level problems, such as multiple simultaneous linear systems and sequences of related linear systems, faster than standard algorithms. The package also supports extended-precision and mixed-precision algorithms. Together, Amesos2 and Belos form a complete suite of sparse linear solvers.

Introduction to Iterative Methods for the Solution of Linear Systems

2017 ◽  
pp. 407-439
Author(s):  
Larisa Beilina ◽  
Evgenii Karchevskii ◽  
Mikhail Karchevskii
Keyword(s):  
Linear Systems ◽  
Iterative Methods
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