Steepest Descent and Conjugate Gradient Methods with Variable Preconditioning

We analyze the conjugate gradient (CG) method with variable preconditioning for solving a linear system with a real symmetric positive definite (SPD) matrix of coefficients $A$. We assume that the preconditioner is SPD on each step, and that the condition number of the preconditioned system matrix i...

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Bibliographic Details
Published in:	SIAM journal on matrix analysis and applications Vol. 29; no. 4; pp. 1267 - 1280
Main Authors:	Knyazev, Andrew V., Lashuk, Ilya
Format:	Journal Article
Language:	English
Published:	Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2007
Subjects:	Acceleration of convergence Algebra Algebraic geometry Algorithms Applied mathematics Exact sciences and technology Iterative methods Linear and multilinear algebra, matrix theory Mathematics Methods Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Sciences and techniques of general use random preconditioning Support conjugate gradient Steepest descent method circular cone Iterative method Iteration variable preconditioning Multigrid Convergence rate Steepest descent Real matrix Conjugate gradient method Cone Grid pattern Solving convergence rate bound Reflection linear systems multigrid; 65F10 Numerical analysis Linear system Symmetric matrix Symmetric system Linear algebra Positive definite matrix Condition number Householder reflection inner-outer iterations preconditioner Preconditioning
ISSN:	0895-4798, 1095-7162
Online Access:	Get full text
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