Solving Sparse Linear Systems with Sparse Backward Error
From MaRDI portal
Publication:4734658
DOI10.1137/0610013zbMath0684.65022OpenAlexW2129256515MaRDI QIDQ4734658
James W. Demmel, Mario Arioli, Iain S. Duff
Publication date: 1989
Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/24271f058dfd64530f733fef3a037794acf5ab9a
condition numbersparse linear systemsLU factorizationiterative refinementbounded perturbationssparsity structurebackward error estimator
Computational methods for sparse matrices (65F50) Numerical computation of matrix norms, conditioning, scaling (65F35) Direct numerical methods for linear systems and matrix inversion (65F05)
Related Items
Perturbation theory and backward error for \(AX - XB = C\), Condition numbers and their condition numbers, Entrywise relative perturbation theory for nonsingular \(M\)-matrices and applications, Accuracy and effectiveness of preconditioned conjugate gradient algorithms for large and ill-conditioned problems, On the augmented system approach to sparse least-squares problems, On the Symmetric Componentwise Relative Backward Error for Linear Systems of Equations, Chebyshev acceleration of iterative refinement, Frequency domain Bernstein-Bézier finite element solver for modelling short waves in elastodynamics, Accelerating the Solution of Linear Systems by Iterative Refinement in Three Precisions, Estimation of the sensitivity of linear and nonlinear algebraic problems, Iterative refinement enhances the stability of \(QR\) factorization methods for solving linear equations, Gaussian elimination: When is scaling beneficial!, Coupling of continuous and hybridizable discontinuous Galerkin methods: application to conjugate heat transfer problem, Bernstein-Bézier based finite elements for efficient solution of short wave problems, Algebraic Error Analysis for Mixed-Precision Multigrid Solvers, Componentwise perturbation theory for linear systems with multiple right- hand sides, Mixed-precision iterative refinement using tensor cores on GPUs to accelerate solution of linear systems, Comparison of high-order continuous and hybridizable discontinuous Galerkin methods for incompressible fluid flow problems, The structured sensitivity of Vandermonde-like systems, Statistical Condition Estimation for Linear Systems, Linear algebra software for large-scale accelerated multicore computing, A survey of direct methods for sparse linear systems, On perturbation bounds of Kronecker product linear systems and their level-2 condition numbers, Error estimation in preconditioned conjugate gradients, Accelerating scientific computations with mixed precision algorithms, A tearing-based hybrid parallel sparse linear system solver, On accurate and time efficient solution of primal-mixed finite element equations in multiscale solid mechanics, Using dual techniques to derive componentwise and mixed condition numbers for a linear function of a linear least squares solution, Perturbation analysis of saddle-point problems, Formation of Finite-Time Singularities in the 3D Axisymmetric Euler Equations: A Numerics Guided Study, Algebraic Error Analysis for Mixed-Precision Multigrid Solvers, Toward the Finite-Time Blowup of the 3D Axisymmetric Euler Equations: A Numerical Investigation, Symbiosis between linear algebra and optimization, Experiments with data perturbations to study condition numbers and numerical stability, Improving Multifrontal Methods by Means of Block Low-Rank Representations, Regularized symmetric indefinite systems in interior point methods for linear and quadratic optimization, Component-wise perturbation analysis and error bounds for linear least squares solutions
Uses Software
