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On a condition for the nonsingularity of a matrix


Author: Alston S. Householder
Journal: Math. Comp. 26 (1972), 119-120
MSC: Primary 65F10
DOI: https://doi.org/10.1090/S0025-5718-1972-0303697-0
MathSciNet review: 0303697
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Abstract: A new derivation of a nonsingularity condition is given and related to conditions for the convergence of a matrix interation.


References [Enhancements On Off] (What's this?)

  • [1] Duane W. Bailey & Douglas E. Crabtree, ``Bounds for determinants,'' Linear Algebra and Appl., v. 2, 1969, pp. 303-309. MR 41 #6864. MR 0262254 (41:6864)
  • [2] V. V. Gudkov, On a Certain Test For Non-Singularity of Matrices, Latvian Math. Yearbook 1965, ``Zinatne", Riga, 1966, pp. 385-390. (Russian) MR 33 #1323. MR 0193102 (33:1323)
  • [3] Alston S. Householder, The Theory of Matrices in Numerical Analysis, Blaisdell, Waltham, Mass., 1964. MR 30 #5475. MR 0175290 (30:5475)
  • [4] 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.
  • [5] Alexander M. Ostrowski, ``Determinanten mit überwiegender Hauptdiagonale und die absolute Konvergenz von linearen Iterationsprozessen,'' Comment. Math. Helv., v. 30, 1956, pp. 175-210. MR 17, 898. MR 0076433 (17:898e)
  • [6] P. Stein & R. L. Rosenberg, ``On the solution of linear simultaneous equations by iteration,'' J. London Math. Soc., v. 23, 1948, pp. 111-118. MR 10, 485. MR 0028682 (10:485b)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1972-0303697-0
Keywords: Matrices, nonsingularity, Gauss-Seidel interation
Article copyright: © Copyright 1972 American Mathematical Society

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