Scaled pivoting in Gauss and Neville elimination for totally positive systems

DOI10.1016/0168-9274(93)90093-7zbMath0796.65022OpenAlexW1966463412MaRDI QIDQ1318374

Mariano Gasca, Juan Manuel Peña

Publication date: 27 March 1994

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-9274(93)90093-7

zbMATH Keywords

Gauss eliminationNeville eliminationscaled partial pivotingtotally positive linear systems

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Numerical computation of matrix norms, conditioning, scaling (65F35) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (12)

Factorizations of confluent Cauchy-Vandermonde matrices ⋮ Inverse central ordering for the Newton interpolation formula ⋮ Tests for the recognition of total positivity ⋮ Analyzing scalability of Neville elimination ⋮ Sign regular matrices and Neville elimination ⋮ The work of Mariano Gasca ⋮ Comparing pivoting strategies for almost strictly sign regular matrices ⋮ Neville elimination: An efficient algorithm with application to chemistry ⋮ Componentwise backward error analysis of Neville elimination ⋮ Backward error analysis of Neville elimination ⋮ Neville elimination: a study of the efficiency using checkerboard partitioning ⋮ A collection of examples where Neville elimination outperforms Gaussian elimination

Cites Work

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• A geometric analysis of Gaussian elimination. I
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• Total positivity and Neville elimination
• Almost strictly totally positive matrices
• Some properties of totally positive matrices
• Backward error analysis for totally positive linear systems
• A matricial description of Neville elimination with applications to total positivity
• Shape preserving representations and optimality of the Bernstein basis
• The LU-factorization of totally positive matrices
• Total Positivity, $QR$ Factorization, and Neville Elimination
• Error Analysis of Direct Methods of Matrix Inversion
• Scaling for Numerical Stability in Gaussian Elimination
• A Hurwitz Matrix is Totally Positive
• The Accuracy of Solutions to Triangular Systems
• Totally positive matrices

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