Householder's tridiagonalization of a symmetric matrix

DOI10.1007/BF02161841zbMath0176.13402OpenAlexW2037324677MaRDI QIDQ2533490

Christian H. Reinsch, J. H. Wilkinson, R. S. Martin

Publication date: 1968

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

Full work available at URL: https://eudml.org/doc/131819

zbMATH Keywords

numerical analysis

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Optimal testing for equicorrelated linear regression models, Two-sided approximations in the LR-algorithm, Computational methods of linear algebra, Extensions and Applications of the Householder Algorithm for Solving Linear Least Squares Problems, A Stable, Rational QR Algorithm for the Computation of the Eigenvalues of an Hermitian, Tridiagonal Matrix, Verfahren für die Bestimmung von Eigenwerten und Eigenvektoren von symmetrisch nicht-hermiteschen Matrizen, The choleski Q.I.F. algorithm for solving symmetric linear systems, Reduction of the symmetric eigenproblem \(Ax =\lambda Bx\) and related problems to standard form, The implicit QL algorithm, Singular value decomposition and least squares solutions, Similarity reduction of a general matrix to Hessenberg form, Stationary values of the ratio of quadratic forms subject to linear constraints, Simultaneous iteration method for symmetric matrices, On the application of eigenvector expansions to numerical deconvolution

Cites Work

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• Householder's method for symmetric matrices
• Calculation of the eigenvectors of a symmetric tridiagonal matrix by inverse iteration
• The QR and QL algorithms for symmetric matrices
• Rational QR transformation with Newton shift for symmetric tridiagonal matrices
• An error analysis of Householder's method for the symmetric eigenvalue problem
• Calculation of the eigenvalues of a symmetric tridiagonal matrix by the method of bisection