A new approach for computing the solution of Sylvester matrix equation

Sadeghi, Amir

doi:10.5899/2016/jiasc-00094

Cited by 1 publication

(1 citation statement)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Many researchers have developed such iterative methods for solving a class of matrix Equations (1)- (4); see e.g., [4][5][6][7][8][9][10]. One of an interesting iterative method, called the Hermitian and skew Hermitian splitting iterative method (HSS), was investigated by many authors, e.g., [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Gradient Iterative Method with Optimal Convergent Factor for Solving a Generalized Sylvester Matrix Equation with Applications to Diffusion Equations

Boonruangkan

Chansangiam

2020

Symmetry

View full text Add to dashboard Cite

We introduce a gradient iterative scheme with an optimal convergent factor for solving a generalized Sylvester matrix equation ∑i=1pAiXBi=F, where Ai,Bi and F are conformable rectangular matrices. The iterative scheme is derived from the gradients of the squared norm-errors of the associated subsystems for the equation. The convergence analysis reveals that the sequence of approximated solutions converge to the exact solution for any initial value if and only if the convergent factor is chosen properly in terms of the spectral radius of the associated iteration matrix. We also discuss the convergent rate and error estimations. Moreover, we determine the fastest convergent factor so that the associated iteration matrix has the smallest spectral radius. Furthermore, we provide numerical examples to illustrate the capability and efficiency of this method. Finally, we apply the proposed scheme to discretized equations for boundary value problems involving convection and diffusion.

show abstract