Convergent generalized monotone splitting of matrices
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- by O. L. Mangasarian PDF
- Math. Comp. 25 (1971), 649-653 Request permission
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
- 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
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Math. Comp. 25 (1971), 649-653
- MSC: Primary 65F30
- DOI: https://doi.org/10.1090/S0025-5718-1971-0298907-1
- MathSciNet review: 0298907