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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


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


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 $SM = TS$.
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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.
  • J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965. MR 0184422
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Math. Comp. 26 (1972), 121-128
  • MSC: Primary 65F15
  • DOI:
  • MathSciNet review: 0309290