Generalized conjugate gradient squared
نویسندگان
چکیده
منابع مشابه
Generalized conjugate gradient squared
The Conjugate Gradient Squared (CGS) is an iterative method for solving nonsymmetric linear systems of equations. However, during the iteration large residual norms may appear, which may lead to inaccurate approximate solutions or may even deteriorate the convergence rate. Instead of squaring the Bi-CG polynomial as in CGS, we propose to consider products of two nearby Bi-CG polynomials which l...
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The Conjugate Gradient Squared (CGS) is a well-known and widely used iterative method for solving non-symmetric linear systems of equations. In practice the method converges fast, often twice as fast as the Bi-Conjugate Gradient (Bi-CG) method. However, during the iteration large residual norms may appear, which may lead to inaccurate approximate solutions or may even deteriorate the convergenc...
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where F (ξ) is a nonlinear operator from a real Euclidean space of dimension n or Hilbert space into itself. The Euclidean norm and corresponding inner product will be denoted by ‖·‖1 and (·, ·)1 respectively. A general different inner product with a weight function and the corresponding norm will be denoted by (·, ·)0 and ‖ · ‖ respectively. In the first part of this article (Sects. 2 and 3) w...
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This paper presents a parallel version of a Generalized Conjugate Gradient algorithm proposed by Liu and Story in which the search direction considers the effect of the inexact line search. We describe the implementation of this algorithm on a parallel architecture and analyze the related speedup ratios. Numerical results are given for a shared memory computer (Cray C92).
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The conjugate gradient squared (CGS) algorithm is a Krylov subspace algorithm that can be used to obtain fast solutions for linear systems (Ax = b) with complex nonsymmetric, very large, and very sparse coeecient matrices (A). By considering electromagnetic scattering problems as examples, a study of the performance and scalability of this algorithm on two MIMD machines is presented. A modiied ...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1996
ISSN: 0377-0427
DOI: 10.1016/0377-0427(95)00227-8