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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Tridiagonalization of completely nonnegative matrices
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by J. W. Rainey and G. J. Habetler PDF
Math. Comp. 26 (1972), 121-128 Request permission

Abstract:

Let $M = [{m_{ij}}]_{i,j = 1}^n$ be completely nonnegative (CNN), i.e., every minor of $M$ is nonnegative. Two methods for reducing the eigenvalue problem for $M$ to that of a CNN, tridiagonal matrix, $T = [{t_{ij}}]$ (${t_{ij}} = 0$ when $|i - j| > 1)$), are presented in this paper. In the particular case that $M$ is nonsingular it is shown for one of the methods that there exists a CNN nonsingular $S$ such that $SM = TS$.
References
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  • F. R. Gantmacher, Matrizenrechnung. II. Spezielle Fragen und Anwendungen, Hochschulbücher für Mathematik, Band 37, VEB Deutscher Verlag der Wissenschaften, Berlin, 1959 (German). MR 0107647
  • F. R. Gantmacher & M. G. KREĬN, Oscillating Matrices and Kernels and Small Oscillations of Mechanical Systems, 2nd ed., GITTL, Moscow, 1950; German transl., AkademieVerlag, Berlin, 1960. MR 14, 178; MR 22 #5161.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Math. Comp. 26 (1972), 121-128
  • MSC: Primary 65F15
  • DOI: https://doi.org/10.1090/S0025-5718-1972-0309290-8
  • MathSciNet review: 0309290