The structured sensitivity of Vandermonde-like systems

DOI10.1007/BF01396218zbMath0766.65042MaRDI QIDQ1203409

Sven G. Bartels, Desmond J. Higham

Publication date: 8 February 1993

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133640

zbMATH Keywords

perturbationsleast squaresmatrix inversioncondition numbersbackward errorsVandermonde-like matrices

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Numerical computation of matrix norms, conditioning, scaling (65F35) Direct numerical methods for linear systems and matrix inversion (65F05) Conditioning of matrices (15A12)

Related Items

Inversion error, condition number, and approximate inverses of uncertain matrices, The condition of Steffensen's acceleration in several variables, Structured mixed and componentwise condition numbers of some structured matrices, Structured condition numbers of structured Tikhonov regularization problem and their estimations

Uses Software

• Algorithm 674
• SONEST
• CONEST

Cites Work

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• Component-wise perturbation analysis and error bounds for linear least squares solutions
• Convergence of a subgradient method for computing the bound norm of matrices
• Error analysis of the Björck-Pereyra algorithms for solving Vandermonde systems
• New condition numbers for matrices and linear systems
• Componentwise perturbation theory for linear systems with multiple right- hand sides
• Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides
• Stability Analysis of Algorithms for Solving Confluent Vandermonde-Like Systems
• Condition Estimates
• Matrix Analysis
• FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation
• Scaling for Numerical Stability in Gaussian Elimination
• Backward Error and Condition of Structured Linear Systems
• The Strong Stability of Algorithms for Solving Symmetric Linear Systems
• Solving Sparse Linear Systems with Sparse Backward Error
• Solution of Vandermonde systems of equations
• Associated Polynomials and Uniform Methods for the Solution of Linear Problems