On the purely algebraic data-sparse approximation of the inverse and the triangular factors of sparse matrices

DOI10.1002/nla.714zbMath1249.65055OpenAlexW2016812335MaRDI QIDQ2889373

Mario Bebendorf, Thomas Fischer

Publication date: 7 June 2012

Published in: Numerical Linear Algebra with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/nla.714

zbMATH Keywords

numerical examplesfinite element discretizationsparse matricesinverseLU decompositionhierarchical matrixlogarithmic-linear complexitybounded condition numbersmatrix partitioning algorithm

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of matrix norms, conditioning, scaling (65F35) Complexity and performance of numerical algorithms (65Y20) Direct numerical methods for linear systems and matrix inversion (65F05)

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A Hierarchical Low Rank Schur Complement Preconditioner for Indefinite Linear Systems ⋮ Hierarchical matrix approximation with blockwise constraints ⋮ Matrices with Hierarchical Low-Rank Structures ⋮ On the spectral equivalence of hierarchical matrix preconditioners for elliptic problems

Cites Work

• Unnamed Item
• Hierarchical matrices. A means to efficiently solve elliptic boundary value problems
• Inverses of banded matrices
• A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices
• A comparative study of sparse approximate inverse preconditioners
• A fast direct algorithm for the solution of the Laplace equation on regions with fractal boundaries
• Existence of \(\mathcal H\)-matrix approximants to the inverse FE-matrix of elliptic operators with \(L^\infty\)-coefficients
• Construction and arithmetics of \(\mathcal H\)-matrices
• Hierarchical matrices based on a weak admissibility criterion
• A sparse \({\mathcal H}\)-matrix arithmetic. II: Application to multi-dimensional problems
• Why Finite Element Discretizations Can Be Factored by Triangular Hierarchical Matrices
• A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
• Parallel Preconditioning with Sparse Approximate Inverses
• A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems
• Approximate Inverse Preconditioners via Sparse-Sparse Iterations
• A Priori Sparsity Patterns for Parallel Sparse Approximate Inverse Preconditioners
• Efficient inversion of the Galerkin matrix of general second-order elliptic operators with nonsmooth coefficients
• Nested Dissection of a Regular Finite Element Mesh

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