article

The numerically stable reconstruction of Jacobi matrices from spectral data

Authors:

William B. Gragg and

William J. HarrodAuthors Info & Claims

Numerische Mathematik, Volume 44, Issue 3

Pages 317 - 335

https://doi.org/10.1007/BF01405565

Published: 01 October 1984 Publication History

Abstract

We present an exposé of the elementary theory of Jacobi matrices and, in particular, their reconstruction from the Gaussian weights and abscissas. Many recent works propose use of the diagonal Hermitian Lanczos process for this purpose. We show that this process is numerically unstable. We recall Rutishauser's elegant and stable algorithm of 1963, based on plane rotations, implement it efficiently, and discuss our numerical experience. We also apply Rutishauser's algorithm to reconstruct a persymmetric Jacobi matrix from its spectrum in an efficient and stable manner.

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Index Terms

The numerically stable reconstruction of Jacobi matrices from spectral data
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Linear algebra algorithms
2. Theory of computation
  1. Design and analysis of algorithms

Index terms have been assigned to the content through auto-classification.

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cover image Numerische Mathematik

Numerische Mathematik Volume 44, Issue 3

October 1984

152 pages

ISSN:0029-599X

Issue’s Table of Contents

Copyright © Copyright © 1984 Springer-Verlag.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 October 1984

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Meurant GTichý P(2023)The behavior of the Gauss-Radau upper bound of the error norm in CGNumerical Algorithms10.1007/s11075-023-01522-z94:2(847-876)Online publication date: 17-Apr-2023
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