Bidiagonal decomposition of rectangular totally positive Said-Ball-Vandermonde matrices: error analysis, perturbation theory and applications

DOI10.1016/j.laa.2016.01.037zbMath1333.65028OpenAlexW2292249943MaRDI QIDQ5962838

Ana Marco, José-Javier Martıńez

Publication date: 24 February 2016

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

Full work available at URL: https://doi.org/10.1016/j.laa.2016.01.037

zbMATH Keywords

algorithmerror analysisnumerical experimentVandermonde matrixNeville eliminationtotally positive matrixbidiagonal decompositionhigh relative accuracySaid-Ball basis

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (11)

Characterizations and accurate computations for tridiagonal Toeplitz matrices ⋮ Accurate computations with collocation matrices of the Lupaş-type \((p,q)\)-analogue of the Bernstein basis ⋮ Accurate computation of eigenvalues of generalized sign regular quasi-Said-Ball-Vandermonde matrices ⋮ Bidiagonal decompositions of Vandermonde-type matrices of arbitrary rank ⋮ Accurate computations for eigenvalues of products of Cauchy-polynomial-Vandermonde matrices ⋮ Accurate computation of the Moore-Penrose inverse of strictly totally positive matrices ⋮ Error analysis, perturbation theory and applications of the bidiagonal decomposition of rectangular totally positive h-Bernstein-Vandermonde matrices ⋮ Accurate bidiagonal decomposition of totally positive Cauchy-Vandermonde matrices and applications ⋮ Accurate bidiagonal decomposition of totally positive h-Bernstein-Vandermonde matrices and applications ⋮ Accurate solutions of weighted least squares problems associated with rank-structured matrices ⋮ Least squares problems involving generalized Kronecker products and application to bivariate polynomial regression

Uses Software

• mctoolbox
• TNTool
• CONSURF

Cites Work

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• Backward error analysis of Neville elimination
• Shape preserving properties of the generalised Ball basis
• Accurate computations with Said-Ball-Vandermonde matrices
• Total positivity and Neville elimination
• A matricial description of Neville elimination with applications to total positivity
• Accurate computations with collocation matrices of rational bases
• On the generalized Ball bases
• Accurate SVDs of polynomial Vandermonde matrices involving orthonormal polynomials
• Numerical methods for solving linear least squares problems
• Accurate Computations with Totally Nonnegative Matrices
• Accurate and efficient expression evaluation and linear algebra
• A generalized Ball curve and its recursive algorithm
• Accuracy and Stability of Numerical Algorithms
• Accurate Eigenvalues and SVDs of Totally Nonnegative Matrices
• Accurate computations with totally positive Bernstein-Vandermonde matrices

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