On some new approximate factorization methods for block tridiagonal matrices suitable for vector and parallel processors

DOI10.1016/j.matcom.2008.09.009zbMath1173.65025OpenAlexW2095389029MaRDI QIDQ1013149

Hong Li, Hou-Biao Li, Yong Zhang, Xing-Ping Liu, Ting-Zhu Huang

Publication date: 17 April 2009

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2008.09.009

zbMATH Keywords

numerical experimentspreconditioningparallel algorithmtridiagonal matrixsecond order elliptic equationsapproximate inverse preconditionersapproximate factorization methodsblock tridiagonal H-matricesoil reservoir simulationspolynomial sparse approximatesparse block-tridiagonal linear systemsstair matrix

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Iterative numerical methods for linear systems (65F10)

Related Items (8)

Comparison theorems for splittings of M-matrices in (block) Hessenberg form ⋮ Quadratic spline collocation method and efficient preconditioner for the Helmholtz equation with the Sommerfeld boundary conditions ⋮ A note on preconditioning for the \(3\times 3\) block saddle point problem ⋮ On the inverses of general tridiagonal matrices ⋮ Chebyshev-type methods and preconditioning techniques ⋮ Preconditioners for all-at-once system from the fractional mobile/immobile advection-diffusion model ⋮ A hybrid triangulation method for banded linear systems ⋮ On \(k\)-step CSCS-based polynomial preconditioners for Toeplitz linear systems with application to fractional diffusion equations

Cites Work

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• Some results on sparse block factorization iterative methods
• Lower bounds for the minimum eigenvalue of Hadamard product of an \(M\)-matrix and its inverse
• Additive polynomial preconditions for parallel computers
• Approximate sparsity patterns for the inverse of a matrix and preconditioning
• Block ILU preconditioners for a nonsymmetric block-tridiagonal \(M\)-matrix
• A preconditioned conjugate gradient method on a distributed memory multiprocessor
• Incomplete block factorization preconditioning for linear systems arising in the numerical solution of the Helmholtz equation
• On a new criterion for the H-matrix property
• Inclusion sets for singular values
• An improvement on a new upper bound for moduli of eigenvalues of iterative matrices
• On some subclasses ofP-matrices
• m-Step Preconditioned Conjugate Gradient Methods
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• On Sparse Block Factorization Iterative Methods
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Stair Matrices and Their Generalizations with Applications to Iterative Methods I: A Generalization of the Successive Overrelaxation Method
• Iterative Solution Methods
• Parallel Preconditioning with Sparse Approximate Inverses
• Approximate Inverse Techniques for Block-Partitioned Matrices
• On the Convergence of the Multisplitting Methods for the Linear Complementarity Problem
• Multisplitting Preconditioners Based on Incomplete Choleski Factorizations

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