Robust and Effective eSIF Preconditioning for General Dense SPD Matrices

DOI10.1137/20M1349540MaRDI QIDQ5161769

Jian-Lin Xia

Publication date: 1 November 2021

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.03729

zbMATH Keywords

effectivenessSPD matrixmultilevel schemeenhanced scaling-and-compression strategyeSIF preconditioningunconditional robustness

Mathematics Subject Classification ID

Related Items (2)

Second‐order accurate hierarchical approximate factorizations for solving sparse linear systems ⋮ Convergence Analysis of Inexact Two-Grid Methods: A Theoretical Framework

Uses Software

• STRUMPACK

Cites Work

• Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
• Numerical experiments on the condition number of the interpolation matrices for radial basis functions
• The incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations
• A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices
• Data-sparse approximation by adaptive \({\mathcal H}^2\)-matrices
• Recursively preconditioned hierarchical interpolative factorization for elliptic partial differential equations
• Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method
• An Algebraic Multilevel Preconditioner with Low-Rank Corrections for Sparse Symmetric Matrices
• Parallel Randomized and Matrix-Free Direct Solvers for Large Structured Dense Linear Systems
• Divide and Conquer Low-Rank Preconditioners for Symmetric Matrices
• On the Complexity of Some Hierarchical Structured Matrix Algorithms
• A Fast Randomized Eigensolver with Structured LDL Factorization Update
• Schur complement-based domain decomposition preconditioners with low-rank corrections
• Randomized algorithms for the low-rank approximation of matrices
• Direction-Preserving and Schur-Monotonic Semiseparable Approximations of Symmetric Positive Definite Matrices
• Robust Approximate Cholesky Factorization of Rank-Structured Symmetric Positive Definite Matrices
• Fast algorithms for hierarchically semiseparable matrices
• Effectiveness and robustness revisited for a preconditioning technique based on structured incomplete factorization
• On the Perturbation of the Cholesky Factorization
• Effective and Robust Preconditioning of General SPD Matrices via Structured Incomplete Factorization
• Preserving Positive Definiteness in Hierarchically Semiseparable Matrix Approximations
• Low-Rank Factorizations in Data Sparse Hierarchical Algorithms for Preconditioning Symmetric Positive Definite Matrices
• Diagonally compensated reduction and related preconditioning methods
• New Efficient and Robust HSS Cholesky Factorization of SPD Matrices
• Efficient Construction of an HSS Preconditioner for Symmetric Positive Definite $\mathcal{H}^2$ Matrices
• An Algebraic Sparsified Nested Dissection Algorithm Using Low-Rank Approximations
• Improving Multifrontal Methods by Means of Block Low-Rank Representations
• A Parallel Geometric Multifrontal Solver Using Hierarchically Semiseparable Structure
• A Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using Randomization
• A Fast $ULV$ Decomposition Solver for Hierarchically Semiseparable Representations
• A robust incomplete factorization preconditioner for positive definite matrices
• Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

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