Journal Article10.1007/BF02662024
Stable doubleLR algorithm and its error analysis
TL;DR: The essential relationship between the doubleLR transformation of a normative matrix and theQR transformation of the related symmetric tridiagonal matrix is proved and a stable doubleLR algorithm for doubleLR Transformation of normative matrices is obtained.
read more
Abstract: In this paper, the normative matrices and their doubleLR transformation with origin shifts are defined, and the essential relationship between the doubleLR transformation of a normative matrix and theQR transformation of the related symmetric tridiagonal matrix is proved. We obtain a stable doubleLR algorithm for doubleLR transformation of normative matrices and give the error analysis of our algorithm. The operation number of the stable doubleLR algorithm for normative matrices is only four sevenths of the rationalQR algorithm for real symmetric tridiagonal matrices.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
References
A stable, rational QR algorithm for the computation of the eigenvalues of an Hermitian, tridiagonal matrix
TL;DR: The most efficient program for finding all the eigenvalues of a symmetric matrix is a combination of the Householder tridiagonalization and the QR algorithm, and by avoiding square roots the efficiency of this algorithm can be further increased.
17
Practical throw-back interpolation
TL;DR: In this article, the authors determined precise conditions for the validity of some frequently used throw-back interpolation formulae, such as the Everett-Bessel-Chebyshev formula.