On some ways of approximating inverses of banded matrices in connection with deriving preconditioners based on incomplete block factorizations

DOI10.1007/BF02242922zbMath0691.65017OpenAlexW425393852WikidataQ114233866 ScholiaQ114233866MaRDI QIDQ582807

Panayot S. Vassilevski

Publication date: 1990

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02242922

zbMATH Keywords

algorithmspreconditionerspreconditioned conjugate gradient methodband approximate inversesband symmetric positive definite matricesblock-tridiagonal matricesincomplete block-factorization methodstationary diffusion equations

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Iterative numerical methods for linear systems (65F10) Direct numerical methods for linear systems and matrix inversion (65F05) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

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Cites Work

• Unnamed Item
• Positive definiteness aspects of vectorizable preconditioners
• The block preconditioned conjugate gradient method on vector computers
• On approximate factorization methods for block matrices suitable for vector and parallel processors
• A general incomplete block-matrix factorization method
• Decay rates of inverses of banded M-matrices that are near to Toeplitz matrices
• Block Preconditioning for the Conjugate Gradient Method
• Decay Rates for Inverses of Band Matrices
• Dichotomies for Band Matrices
• An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix