scholarly journals A preconditioned nested splitting conjugate gradient iterative method for the large sparse generalized Sylvester equation

2014 ◽  
Vol 68 (10) ◽  
pp. 1409-1420 ◽  
Author(s):  
Yi-Fen Ke ◽  
Chang-Feng Ma
Keyword(s):  
Iterative Method ◽  
Conjugate Gradient ◽  
Sylvester Equation ◽  
Generalized Sylvester Equation

A symmetric preserving iterative method for generalized Sylvester equation

2010 ◽  
Vol 13 (3) ◽  
pp. 408-417 ◽  
Author(s):  
Jiao-Fen Li ◽  
Xi-Yan Hu ◽  
Xue-Feng Duan
Keyword(s):  
Iterative Method ◽  
Sylvester Equation ◽  
Generalized Sylvester Equation

A Newton-like method for computing deflating subspaces

2015 ◽  
Vol 23 (4) ◽  
Author(s):  
Kirill V. Demyanko ◽  
Yuri M. Nechepurenko ◽  
Miloud Sadkane
Keyword(s):  
Stability Problem ◽  
Initial Guess ◽  
Sylvester Equation ◽  
Gmres Method ◽  
Regular Matrix ◽  
Subspace Iteration ◽  
Generalized Sylvester Equation ◽  
Matrix Pencils ◽  
Deflating Subspaces ◽  
Preconditioned Gmres

AbstractThis work is devoted to computations of deflating subspaces associated with separated groups of finite eigenvalues near specified shifts of large regular matrix pencils. The proposed method is a combination of inexact inverse subspace iteration and Newton’s method. The first one is slow but reliably convergent starting with almost an arbitrary initial subspace and it is used as a preprocessing to obtain a good initial guess for the second method which is fast but only locally convergent. The Newton method necessitates at each iteration the solution of a generalized Sylvester equation and for this task an iterative algorithm based on the preconditioned GMRES method is devised. Numerical properties of the proposed combination are illustrated with a typical hydrodynamic stability problem.

scholarly journals Two Iterative Methods for Solving Linear Interval Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Esmaeil Siahlooei ◽  
Seyed Abolfazl Shahzadeh Fazeli
Keyword(s):  
Iterative Method ◽  
Conjugate Gradient ◽  
Numerical Experiments ◽  
Gradient Algorithm ◽  
Interval Matrix ◽  
Interval Numbers ◽  
Linear Interval ◽  
Linear Interval Systems ◽  
Diagonally Dominant ◽  
Interval Systems

Conjugate gradient is an iterative method that solves a linear system Ax=b, where A is a positive definite matrix. We present this new iterative method for solving linear interval systems Ãx̃=b̃, where à is a diagonally dominant interval matrix, as defined in this paper. Our method is based on conjugate gradient algorithm in the context view of interval numbers. Numerical experiments show that the new interval modified conjugate gradient method minimizes the norm of the difference of Ãx̃ and b̃ at every step while the norm is sufficiently small. In addition, we present another iterative method that solves Ãx̃=b̃, where à is a diagonally dominant interval matrix. This method, using the idea of steepest descent, finds exact solution x̃ for linear interval systems, where Ãx̃=b̃; we present a proof that indicates that this iterative method is convergent. Also, our numerical experiments illustrate the efficiency of the proposed methods.

Application of g-frames in conjugate gradient

2016 ◽  
Vol 7 (3) ◽  
Author(s):  
Hassan Jamali ◽  
Neda Momeni
Keyword(s):  
Hilbert Space ◽  
Iterative Method ◽  
Operator Equation ◽  
Conjugate Gradient ◽  
Separable Hilbert Space

AbstractThis paper proposes an iterative method for solving an operator equation on a separable Hilbert space

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