Efficient Structured Multifrontal Factorization for General Large Sparse Matrices
From MaRDI portal
Publication:5300120
DOI10.1137/120867032zbMath1266.15022OpenAlexW2036564429MaRDI QIDQ5300120
Publication date: 26 June 2013
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/c60d7582a14b9e749a419b8b7363fe91366d7cd3
reduced matrixstructured multifrontal methodHSS matrixgeneral sparse matrixULV factorizationsparse rank relaxation
Lua error in Module:PublicationMSCList at line 37: attempt to index local 'msc_result' (a nil value).
Related Items (45)
Performance study of hierarchical semi-separable compression solver for parabolic problems with space-fractional diffusion ⋮ Existence of $\mathcal {H}$-matrix approximants to the inverses of BEM matrices: The simple-layer operator ⋮ Effective matrix-free preconditioning for the augmented immersed interface method ⋮ A fast block low-rank dense solver with applications to finite-element matrices ⋮ Low-rank improvements of two-level grid preconditioned matrices ⋮ Hierarchical orthogonal factorization: sparse least squares problems ⋮ A Technique for Updating Hierarchical Skeletonization-Based Factorizations of Integral Operators ⋮ Hierarchical Interpolative Factorization for Elliptic Operators: Differential Equations ⋮ Efficient preconditioning of \(hp\)-FEM matrices by hierarchical low-rank approximations ⋮ Distributed-memory hierarchical interpolative factorization ⋮ Fast Sparse Selected Inversion ⋮ A Fast Contour-Integral Eigensolver for Non-Hermitian Matrices ⋮ Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners ⋮ An Incomplete Cholesky Preconditioner Based on Orthogonal Approximations ⋮ A Distributed-Memory Randomized Structured Multifrontal Method for Sparse Direct Solutions ⋮ On the Complexity of the Block Low-Rank Multifrontal Factorization ⋮ A fast, memory efficient and robust sparse preconditioner based on a multifrontal approach with applications to finite‐element matrices ⋮ An \(O(N)\) algorithm for constructing the solution operator to 2D elliptic boundary value problems in the absence of body loads ⋮ Second‐order accurate hierarchical approximate factorizations for solving sparse linear systems ⋮ \(\mathcal {H}\)-matrix approximability of the inverses of FEM matrices ⋮ Fast Factorization Update for General Elliptic Equations Under Multiple Coefficient Updates ⋮ An Algebraic Sparsified Nested Dissection Algorithm Using Low-Rank Approximations ⋮ A Robust Multilevel Approximate Inverse Preconditioner for Symmetric Positive Definite Matrices ⋮ An MSSS-preconditioned matrix equation approach for the time-harmonic elastic wave equation at multiple frequencies ⋮ Bridging the Gap Between Flat and Hierarchical Low-Rank Matrix Formats: The Multilevel Block Low-Rank Format ⋮ A Class of Iterative Solvers for the Helmholtz Equation: Factorizations, Sweeping Preconditioners, Source Transfer, Single Layer Potentials, Polarized Traces, and Optimized Schwarz Methods ⋮ Fast structured LU factorization for nonsymmetric matrices ⋮ An algebraic multifrontal preconditioner that exploits the low‐rank property ⋮ A survey of direct methods for sparse linear systems ⋮ Intrinsic Complexity and Scaling Laws: From Random Fields to Random Vectors ⋮ An Algebraic Multilevel Preconditioner with Low-Rank Corrections for Sparse Symmetric Matrices ⋮ A Fast Memory Efficient Construction Algorithm for Hierarchically Semi-Separable Representations ⋮ Superfast Divide-and-Conquer Method and Perturbation Analysis for Structured Eigenvalue Solutions ⋮ A direct solver for elliptic PDEs in three dimensions based on hierarchical merging of Poincaré-Steklov operators ⋮ Hierarchical Interpolative Factorization for Elliptic Operators: Integral Equations ⋮ \({\mathscr{H}} \)-matrix approximability of inverses of discretizations of the fractional Laplacian ⋮ Efficient preconditioning of \(h p\)-FEM matrix sequences with slowly-varying coefficients: an application to topology optimization ⋮ On the Stability of Some Hierarchical Rank Structured Matrix Algorithms ⋮ A Power Schur Complement Low-Rank Correction Preconditioner for General Sparse Linear Systems ⋮ Improving Multifrontal Methods by Means of Block Low-Rank Representations ⋮ Interconnected hierarchical structures for fast direct elliptic solution ⋮ A Parallel Geometric Multifrontal Solver Using Hierarchically Semiseparable Structure ⋮ A Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using Randomization ⋮ A Hierarchical Preconditioner for Wave Problems in Quasilinear Complexity ⋮ Hierarchical Orthogonal Factorization: Sparse Square Matrices
Uses Software
This page was built for publication: Efficient Structured Multifrontal Factorization for General Large Sparse Matrices
