scholarly journals A Modification of Minimal Residual Iterative Method to Solve Linear Systems

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Xingping Sheng ◽  
Youfeng Su ◽  
Guoliang Chen
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Linear Systems ◽  
Residual Error ◽  
Projection Technique ◽  
Numerical Example ◽  
Minimal Residual

We give a modification of minimal residual iteration (MR), which is 1V-DSMR to solve the linear systemAx=b. By analyzing, we find the modifiable iteration to be a projection technique; moreover, the modification of which gives a better (at least the same) reduction of the residual error than MR. In the end, a numerical example is given to demonstrate the reduction of the residual error between the 1V-DSMR and MR.

Convergence Analysis of Preconditioned SSOR Iterative Method for Linear Systems

2014 ◽  
Vol 644-650 ◽  
pp. 1988-1991
Author(s):  
Ting Zhou
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Convergence Analysis ◽  
Linear Systems ◽  
Iterative Methods ◽  
Convergence Result ◽  
Numerical Example ◽  
Preconditioned Iterative ◽  
Preconditioned Iterative Methods

For solving the linear system, different preconditioned iterative methods have been proposed by many authors. In this paper, we present preconditioned SSOR iterative method for solving the linear systems. Meanwhile, we apply the preconditioner to H-matrix and obtain the convergence result. Finally, a numerical example is also given to illustrate our results.

The Linear System Solver of Programs Named CORTH and KYLIN2

2017 ◽  
Author(s):  
Pingzhou Ming ◽  
Junjie Pan ◽  
Xiaolan Tu ◽  
Dong Liu ◽  
Hongxing Yu
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Nuclear Power ◽  
Experimental Results ◽  
Gmres Method ◽  
Thermal Hydraulics ◽  
Lattice Calculation ◽  
Minimal Residual

Sub-channel thermal-hydraulics program named CORTH and assembly lattice calculation program named KYLIN2 have been developed in Nuclear Power Institute of China (NPIC). For the sake of promoting the computing efficiency of these programs and achieving the better description on fined parameters of reactor, the programs’ structure and details are interpreted. Then the characteristics of linear systems of these programs are analyzed. Based on the Generalized Minimal Residual (GMRES) method, different parallel schemes and implementations are considered. The experimental results show that calculation efficiencies of them are improved greatly compared with the serial situation.

scholarly journals Some Results on Preconditioned Mixed-Type Splitting Iterative Method

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Guangbin Wang ◽  
Fuping Tan
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Rate Of Convergence ◽  
Mixed Type ◽  
Comparison Theorems ◽  
Numerical Example

We present a preconditioned mixed-type splitting iterative method for solving the linear system Ax=b, where A is a Z-matrix. And we give some comparison theorems to show that the rate of convergence of the preconditioned mixed-type splitting iterative method is faster than that of the mixed-type splitting iterative method. Finally, we give one numerical example to illustrate our results.

A Preconditioned AOR Iterative Method for an H-Matrix

2014 ◽  
Vol 644-650 ◽  
pp. 1984-1987
Author(s):  
Shi Guang Zhang
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Triangular Matrix ◽  
Coefficient Matrix ◽  
Numerical Example ◽  
Upper Triangular Matrix

The paper presents a preconditioned AOR iterative method if preconditioner is a general upper triangular matrix for solving a linear system whose coefficient matrix is an H-matrix. In addition, we discuss the convergence of corresponding methods. Finally, a numerical example is also given to illustrate our results.

scholarly journals Descriptor fractional discrete-time linear system with two different fractional orders and its solution

2016 ◽  
Vol 64 (1) ◽  
pp. 15-20 ◽  
Author(s):  
Ł. Sajewski
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Discrete Time ◽  
Decomposition Theorem ◽  
State Equation ◽  
The State ◽  
Extension Method ◽  
Numerical Example ◽  
Fractional Orders ◽  
Time Linear

Abstract Factional Discrete-time linear systems with fractional different orders are addressed. The Weierstrass-Kronecker decomposition theorem of the regular pencil is extended to the descriptor fractional discrete-time linear system with different fractional orders. Using the extension, method for finding the solution of the state equation is derived. Effectiveness of the method is demonstrated on a numerical example.

scholarly journals Stabilization of positive descriptor fractional discrete-time linear system with two different fractional orders by decentralized controller

2017 ◽  
Vol 65 (5) ◽  
pp. 709-714 ◽  
Author(s):  
Ł. Sajewski
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Positive Systems ◽  
Numerical Example ◽  
Necessary And Sufficient ◽  
Fractional Orders ◽  
Time Linear

Abstract Positive descriptor fractional discrete-time linear systems with fractional different orders are addressed in the paper. The decomposition of the regular pencil is used to extend necessary and sufficient conditions for positivity of the descriptor fractional discrete-time linear system with different fractional orders. A method for finding the decentralized controller for the class of positive systems is proposed and its effectiveness is demonstrated on a numerical example.

scholarly journals Properweak regular splitting and its application to convergence of alternating iterations

Filomat ◽  
2018 ◽  
Vol 32 (19) ◽  
pp. 6563-6573 ◽  
Author(s):  
Debasisha Mishra
Keyword(s):  
Linear System ◽  
Convergence Rate ◽  
Iterative Method ◽  
Linear Systems ◽  
Iterative Scheme ◽  
Convergence Theory ◽  
System Of Equations ◽  
Comparison Result ◽  
Linear System Of Equations ◽  
Regular Splitting

Theory of matrix splittings is a useful tool for finding the solution of a rectangular linear system of equations, iteratively. The purpose of this paper is two-fold. Firstly, we revisit the theory of weak regular splittings for rectangular matrices. Secondly, we propose an alternating iterative method for solving rectangular linear systems by using the Moore-Penrose inverse and discuss its convergence theory, by extending the work of Benzi and Szyld [Numererische Mathematik 76 (1997) 309-321; MR1452511]. Furthermore, a comparison result is obtained which ensures the faster convergence rate of the proposed alternating iterative scheme.

Comparison Results on Preconditioned AOR-Type Iterative Method for M-Matrices

2013 ◽  
Vol 756-759 ◽  
pp. 2629-2633
Author(s):  
Ting Zhou ◽  
Hong Fang Cui
Keyword(s):  
Linear System ◽  
Convergence Rate ◽  
Iterative Method ◽  
Iterative Methods ◽  
Science And Engineering ◽  
Numerical Example ◽  
Comparison Results ◽  
Preconditioned Iterative ◽  
Preconditioned Iterative Methods

For solving the linear system, different preconditioned iterative methods have been proposed by many authors. M-matrices appear in many areas of science and engineering. In this paper, we present preconditioned AOR-type iterative method and the SOR-type iterative method with a preconditioner for solving the M-matrices. In addition, the relation between the convergence rate of preconditioned AOR-type iterative method and the parameters are brought to light. Finally, a numerical example is also given to illustrate the results.

scholarly journals Design of regular positive and stable descriptor systems via state-feedbacks for descriptor continuous-time linear systems with singular pencils

2014 ◽  
Vol 24 (3) ◽  
pp. 289-297
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Special Form ◽  
The State ◽  
New Method ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Asymptotically Stable ◽  
Numerical Example ◽  
Time Linear

Abstract A new method is proposed of design of regular positive and asymptotically stable descriptor systems by the use of state-feedbacks for descriptor continuous-time linear systems with singular pencils. The method is based on the reduction of the descriptor system by elementary row and column operations to special form. A procedure for the design of the state-feedbacks gain matrix is presented and illustrated by a numerical example

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