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

2015 ◽  
Vol 23 (4) ◽  
Author(s):  
Kirill V. Demyanko ◽  
Yuri M. Nechepurenko ◽  
Miloud Sadkane

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.


2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Esmaeil Siahlooei ◽  
Seyed Abolfazl Shahzadeh Fazeli

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.


2016 ◽  
Vol 7 (3) ◽  
Author(s):  
Hassan Jamali ◽  
Neda Momeni

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


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