A Comparative Study of Iterative Solvers Exploiting Spectral Information for SPD Systems

When solving the symmetric positive definite (SPD) linear system ${\bf A} {\bf x}^\star = {\bf b}$ with the conjugate gradient method, the smallest eigenvalues in the matrix ${\bf A}$ often slow down the convergence. Consequently if the smallest eigenvalues in ${\bf A}$ could somehow be "remove...

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Bibliographic Details
Published in:	SIAM journal on scientific computing Vol. 27; no. 5; pp. 1760 - 1786
Main Authors:	Giraud, Luc, Ruiz, Daniel, Touhami, Ahmed
Format:	Journal Article
Language:	English
Published:	Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2006
Subjects:	Algorithms Eigenvalues Exact sciences and technology Mathematics Nonlinear algebraic and transcendental equations Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Partial differential equations, boundary value problems Sciences and techniques of general use Invariant subspace Decomposition method Eigenvalue Iterative method Partial differential equation Direct method Finite element method 65F50 Efficiency Multigrid two-grid schemes Convergence rate 65F15 65H10 iterative methods; 65F10 Conjugate gradient method Spectral method Filtering Convergence acceleration Numerical linear algebra Chebyshev polynomial Initial value problem Computational complexity Factorization Discretization method block Lanczos method Sensitivity Numerical analysis Boundary value problem Linear system Scientific computation Matrix inversion Deflation spectral preconditioning Domain decomposition Preconditioning 65N22 Chebyshev polynomials
ISSN:	1064-8275, 1095-7197
Online Access:	Get full text
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