Gaussian elimination: When is scaling beneficial!

DOI10.1016/0024-3795(92)90382-KzbMath0748.65026OpenAlexW2072251076MaRDI QIDQ1183194

Larry Neal, George D. Poole

Publication date: 28 June 1992

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(92)90382-k

zbMATH Keywords

Gaussian eliminationscalingpartial pivotingequilibrationback substitution phasesweepout phase

Mathematics Subject Classification ID

Numerical computation of matrix norms, conditioning, scaling (65F35) Direct numerical methods for linear systems and matrix inversion (65F05) Conditioning of matrices (15A12)

Related Items (3)

A geometric analysis of Gaussian elimination. II ⋮ A geometric analysis of Gaussian elimination. I ⋮ The Rook's pivoting strategy

Uses Software

• LINPACK
• NAPACK

Cites Work

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• A geometric analysis of Gaussian elimination. I
• Optimally scaled matrices
• A geometric analysis of Gaussian elimination. II
• The Rook's pivoting strategy
• Condition numbers and equilibration of matrices
• Condition, equilibration and pivoting in linear algebraic systems
• Average-Case Stability of Gaussian Elimination
• Error Analysis of Direct Methods of Matrix Inversion
• Scaling for Numerical Stability in Gaussian Elimination
• Iterative Refinement Implies Numerical Stability for Gaussian Elimination
• Effect of Equilibration on Residual Size for Partial Pivoting
• The Accuracy of Solutions to Triangular Systems
• Solving Sparse Linear Systems with Sparse Backward Error
• Modern Error Analysis

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