scholarly journals On preconditioned normal and skew-Hermitian splitting iteration method for continuous Sylvester equations AX + XB = C*

Filomat ◽  
2018 ◽  
Vol 32 (6) ◽  
pp. 2207-2217
Author(s):  
Xue-Qing Liang ◽  
Xiang Wang ◽  
Xiao-Bin Tang ◽  
Xiao-Yong Xiao
Keyword(s):  
Exact Solution ◽  
Theoretical Analysis ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Convergence Property ◽  
Positive Definite ◽  
New Method ◽  
Splitting Iteration Method

In this paper, we present a preconditioned normal and skew-Hermitian splitting (PNSS) iteration method for continuous Sylvester equations AX + XB = C with positive definite/semi-definite matrices. Theoretical analysis shows that the PNSS methods will converge unconditionally to the exact solution of the continuous Sylvester equations. An inexact variant of the PNSS iteration method(IPNSS) and the analysis of its convergence property in detail have been established. Numerical experiments further show that this new method is more efficient and robust than the existing ones.

scholarly journals Two-step modulus-based matrix splitting iteration method for horizontal linear complementarity problems

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2171-2184
Author(s):  
Lu Jia ◽  
Xiang Wang ◽  
Xuan-Sheng Wang
Keyword(s):  
Theoretical Analysis ◽  
Linear Complementarity Problem ◽  
Iteration Method ◽  
Complementarity Problem ◽  
Numerical Experiments ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Matrix Splitting ◽  
Splitting Iteration Method

The modulus-based matrix splitting iteration has received substantial attention as a momentous tool for complementarity problems. For the purpose of solving the horizontal linear complementarity problem, we introduce the two-step modulus-based matrix splitting iteration method. We also show the theoretical analysis of the convergence. Numerical experiments illustrate the effectiveness of the proposed approach.

Preconditioned Positive-Definite and Skew-Hermitian Splitting Iteration Methods for Continuous Sylvester Equations AX + XB = C

2017 ◽  
Vol 7 (1) ◽  
pp. 55-69 ◽  
Author(s):  
Rong Zhou ◽  
Xiang Wang ◽  
Xiao-Bin Tang
Keyword(s):  
Iteration Method ◽  
Convergence Property ◽  
Positive Definite ◽  
Numerical Results ◽  
New Method ◽  
Iteration Methods

AbstractIn this paper, we present a preconditioned positive-definite and skew-Hermitian splitting (PPSS) iteration method for continuous Sylvester equations AX + XB = C with positive definite/semi-definite matrices. The analysis shows that the PPSS iteration method will converge under certain assumptions. An inexact variant of the PPSS iteration method (IPPSS) has been presented and the analysis of its convergence property in detail has been discussed. Numerical results show that this new method is more efficient and robust than the existing ones.

scholarly journals A Simpler GMRES Method for Oscillatory Integrals with Irregular Oscillations

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Qinghua Wu ◽  
Meiying Xiang
Keyword(s):  
Theoretical Analysis ◽  
Matrix Factorization ◽  
Numerical Experiments ◽  
Oscillatory Integral ◽  
Oscillatory Integrals ◽  
New Method ◽  
Gmres Method ◽  
Hessenberg Matrix

A simpler GMRES method for computing oscillatory integral is presented. Theoretical analysis shows that this method is mathematically equivalent to the GMRES method proposed by Olver (2009). Moreover, the simpler GMRES does not require upper Hessenberg matrix factorization, which leads to much simpler program and requires less work. Numerical experiments are conducted to illustrate the performance of the new method and show that in some cases the simpler GMRES method could achieve higher accuracy than GMRES.

scholarly journals Two-step Tensor Splitting Iteration Method for Multi-linear Systems

2021 ◽  
pp. 48-55
Author(s):  
Bing Cheng ◽  
Guangbin Wang ◽  
Fuping Tan
Keyword(s):  
Convergence Analysis ◽  
Linear Systems ◽  
Iteration Method ◽  
New Method ◽  
Numerical Examples ◽  
Splitting Iteration Method

In this paper, we construct two-step tensor splitting iteration method for multi-linear systems. Moreover, we present convergence analysis of this method. Finally, we give two numerical examples to show that this new method is more ecient than the existing methods.

A Fast Shift-Splitting Iteration Method for Nonsymmetric Saddle Point Problems

2017 ◽  
Vol 7 (1) ◽  
pp. 172-191 ◽  
Author(s):  
Quan-Yu Dou ◽  
Jun-Feng Yin ◽  
Ze-Yu Liao
Keyword(s):  
Saddle Point ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Saddle Point Problems ◽  
Splitting Technique ◽  
Splitting Iteration Method

AbstractBased on the shift-splitting technique and the idea of Hermitian and skew-Hermitian splitting, a fast shift-splitting iteration method is proposed for solving nonsingular and singular nonsymmetric saddle point problems in this paper. Convergence and semi-convergence of the proposed iteration method for nonsingular and singular cases are carefully studied, respectively. Numerical experiments are implemented to demonstrate the feasibility and effectiveness of the proposed method.

scholarly journals Solvability Theory and Iteration Method for One Self-Adjoint Polynomial Matrix Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Zhigang Jia ◽  
Meixiang Zhao ◽  
Minghui Wang ◽  
Sitao Ling
Keyword(s):  
Iterative Algorithm ◽  
Perturbation Analysis ◽  
Matrix Equation ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Polynomial Matrix ◽  
Sufficient Conditions ◽  
Positive Definite ◽  
Solvability Theory ◽  
Adjoint Polynomial

The solvability theory of an important self-adjoint polynomial matrix equation is presented, including the boundary of its Hermitian positive definite (HPD) solution and some sufficient conditions under which the (unique or maximal) HPD solution exists. The algebraic perturbation analysis is also given with respect to the perturbation of coefficient matrices. An efficient general iterative algorithm for the maximal or unique HPD solution is designed and tested by numerical experiments.

scholarly journals ConceFT: concentration of frequency and time via a multitapered synchrosqueezed transform

2016 ◽  
Vol 374 (2065) ◽  
pp. 20150193 ◽  
Author(s):  
Ingrid Daubechies ◽  
Yi (Grace) Wang ◽  
Hau-tieng Wu
Keyword(s):  
Theoretical Analysis ◽  
Numerical Experiments ◽  
Time Dependent ◽  
New Method ◽  
Time Varying ◽  
Frequency Content ◽  
Time Frequency ◽  
Instantaneous Frequencies

A new method is proposed to determine the time–frequency content of time-dependent signals consisting of multiple oscillatory components, with time-varying amplitudes and instantaneous frequencies. Numerical experiments as well as a theoretical analysis are presented to assess its effectiveness.

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