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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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On a condition for the nonsingularity of a matrix
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by Alston S. Householder PDF
Math. Comp. 26 (1972), 119-120 Request permission

Abstract:

A new derivation of a nonsingularity condition is given and related to conditions for the convergence of a matrix interation.
References
  • Duane W. Bailey and Douglas E. Crabtree, Bounds for determinants, Linear Algebra Appl. 2 (1969), 303–309. MR 262254, DOI 10.1016/0024-3795(69)90032-9
  • V. V. Gudkov, On a certain test for non-singularity of matrices, Latvian Math. Yearbook 1965 (Russian), Izdat. “Zinatne”, Riga, 1966, pp. 385–390 (Russian, with Latvian and English summaries). MR 0193102
  • Alston S. Householder, The theory of matrices in numerical analysis, Blaisdell Publishing Co. [Ginn and Co.], New York-Toronto-London, 1964. MR 0175290
  • R. Mehmke, K sposobu Zeĭdelja, služaščemu dlja rešenija sistemy lineĭnyh uravneniĭ s ves’ma bol’šym čislom neizvestnyh posredstvom posledovatel’nyh približeniĭ. Izvlečenie iz pis’ma professoru Memke k professoru Nekrasovu (On Seidel’s method for the solution of a system of linear equations with a large number of unknowns by means of approximations. From a letter from Professor Mehmke to Professor Nekrasov (in German).), Mat. Sb, v. 16, 1892, pp. 342-345.
  • Alexander Ostrowski, Determinanten mit überwiegender Hauptdiagonale und die absolute Konvergenz von linearen Iterationsprozessen, Comment. Math. Helv. 30 (1956), 175–210 (German). MR 76433, DOI 10.1007/BF02564340
  • P. Stein and R. L. Rosenberg, On the solution of linear simultaneous equations by iteration, J. London Math. Soc. 23 (1948), 111–118. MR 28682, DOI 10.1112/jlms/s1-23.2.111
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Math. Comp. 26 (1972), 119-120
  • MSC: Primary 65F10
  • DOI: https://doi.org/10.1090/S0025-5718-1972-0303697-0
  • MathSciNet review: 0303697