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Convergent generalized monotone splitting of matrices


Author: O. L. Mangasarian
Journal: Math. Comp. 25 (1971), 649-653
MSC: Primary 65F30
DOI: https://doi.org/10.1090/S0025-5718-1971-0298907-1
MathSciNet review: 0298907
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Abstract: Let B and T be $ n \times n$ real matrices and r an n-vector and consider the system $ u = BTu + r$. A new sufficient condition is given for the existence of a solution and convergence of a monotone process to a solution. The monotone process is a generalization of the Collatz-Schröder procedure.


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

  • [1] L. Collatz, Funktionalanalysis und numerische Mathematik, Die Grundlehren der math. Wissenschaften, Band 120, Springer-Verlag, Berlin, 1964; English transl., Academic Press, New York, 1966, pp. 350-390. MR 34 #4961. MR 0165651 (29:2931)
  • [2] O. L. Mangasarian, ``Characterizations of real matrices of monotone kind,'' SIAM Rev., v. 10, 1968, pp. 439-441. MR 38 #5818. MR 0237537 (38:5818)
  • [3] O. L. Mangasarian, Nonlinear Programming, McGraw-Hill, New York, 1969, pp. 28-29. MR 40 #5263. MR 0252038 (40:5263)
  • [4] T. S. Motzkin, Beiträge zur Theorie der Linearen Ungleichungen, Inaugural Dissertation, Basel, Jerusalem, 1936.
  • [5] R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, N. J., 1962. MR 28 #1725. MR 0158502 (28:1725)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1971-0298907-1
Keywords: Monotone splitting of matrices, linear inequalities
Article copyright: © Copyright 1971 American Mathematical Society

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