Accurate and efficient expression evaluation and linear algebra

DOI10.1017/S0962492906350015zbMath1169.65022arXiv0712.4027OpenAlexW2156792823MaRDI QIDQ3612041

Plamen Koev, Ioana Dumitriu, James W. Demmel, O. V. Holtz

Publication date: 3 March 2009

Published in: Acta Numerica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.4027

zbMATH Keywords

algorithmscomputational complexityeigenvaluesaccuracysurvey papernumerical linear algebraSchur complementsmatrix inversiontotally non-negative matricesevaluation of multivariate polynomialsmachine epsilontraditional model of arithmetic

Mathematics Subject Classification ID

Related Items (27)

Accurate determinants of some classes of matrices ⋮ Characterizations and accurate computations for tridiagonal Toeplitz matrices ⋮ Accurate solutions of product linear systems associated with rank-structured matrices ⋮ A periodic qd-type reduction for computing eigenvalues of structured matrix products to high relative accuracy ⋮ Accurate computations with collocation matrices of the Lupaş-type \((p,q)\)-analogue of the Bernstein basis ⋮ Accurate bidiagonal decomposition and computations with generalized Pascal matrices ⋮ Accurate eigenvalues of some generalized sign regular matrices via relatively robust representations ⋮ Accurate inverses of Nekrasov \(Z\)-matrices ⋮ On the accuracy of de Casteljau-type algorithms and Bernstein representations ⋮ Accurate computations for eigenvalues of products of Cauchy-polynomial-Vandermonde matrices ⋮ The accurate and efficient solutions of linear systems for generalized sign regular matrices with certain signature ⋮ Unnamed Item ⋮ 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 singular values of a class of parameterized negative matrices ⋮ Accurate Computations and Applications of Some Classes of Matrices ⋮ Accurate bidiagonal decomposition of totally positive Cauchy-Vandermonde matrices and applications ⋮ Accurate computations with Said-Ball-Vandermonde matrices ⋮ Accurate bidiagonal decomposition of totally positive h-Bernstein-Vandermonde matrices and applications ⋮ Accurate solutions of weighted least squares problems associated with rank-structured matrices ⋮ Accurate solutions of structured generalized Kronecker product linear systems ⋮ Accurate computations of eigenvalues of quasi-Cauchy-Vandermonde matrices ⋮ Bidiagonal decomposition of rectangular totally positive Said-Ball-Vandermonde matrices: error analysis, perturbation theory and applications ⋮ Numerical methods for accurate computation of the eigenvalues of Hermitian matrices and the singular values of general matrices ⋮ A qd-type method for computing generalized singular values of BF matrix pairs with sign regularity to high relative accuracy ⋮ Computing eigenvalues of quasi-generalized Vandermonde matrices to high relative accuracy ⋮ Accurate Computation of Generalized Eigenvalues of Regular SR-BP Pairs

Uses Software

• LAPACK
• Hull

Cites Work

• LAPACK Users' Guide
• Lectures on Polytopes
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