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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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Convergent generalized monotone splitting of matrices
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by O. L. Mangasarian PDF
Math. Comp. 25 (1971), 649-653 Request permission


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.
  • Lothar Collatz, Funktionalanalysis und numerische Mathematik, Die Grundlehren der mathematischen Wissenschaften, Band 120, Springer-Verlag, Berlin, 1964 (German). MR 0165651
  • O. L. Mangasarian, Characterizations of real matrices of monotone kind, SIAM Rev. 10 (1968), 439–441. MR 237537, DOI 10.1137/1010095
  • Olvi L. Mangasarian, Nonlinear programming, McGraw-Hill Book Co., New York-London-Sydney, 1969. MR 0252038
  • T. S. Motzkin, Beiträge zur Theorie der Linearen Ungleichungen, Inaugural Dissertation, Basel, Jerusalem, 1936.
  • Richard S. Varga, Matrix iterative analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0158502
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Math. Comp. 25 (1971), 649-653
  • MSC: Primary 65F30
  • DOI:
  • MathSciNet review: 0298907