A steepest ascent method for the Chebyshev problem
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- by Marcel Meicler PDF
- Math. Comp. 23 (1969), 813-817 Request permission
Abstract:
In this paper we present an efficient ascent method for calculating the minimax solution of an overdetermined system of linear equations $Ax = b$. The algorithm makes best use of all the information available at each cycle in order to force a very steep path to the solution.References
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T. L. Boullion & P. L. Odell, An Introduction to the Theory of Generalized Matrix Invertibility, Texas Center for Research, 1966, p. 120.
- Richard H. Bartels and Gene H. Golub, Stable numerical methods for obtaining the Chebyshev solution to an overdetermined system of equations, Comm. ACM 11 (1968), 401–406. MR 0240957, DOI 10.1145/363347.363364
- E. W. Cheney, Introduction to approximation theory, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0222517
- Randall E. Cline, Representations for the generalized inverse of a partitioned matrix, J. Soc. Indust. Appl. Math. 12 (1964), 588–600. MR 172890
- T. N. E. Greville, Some applications of the pseudoinverse of a matrix, SIAM Rev. 2 (1960), 15–22. MR 110185, DOI 10.1137/1002004
- D. C. Handscomb (ed.), Methods of numerical approximation, Pergamon Press, Oxford-New York-Toronto, Ont., 1966. Lectures delivered at a Summer School held at Oxford University, Oxford, September, 1965. MR 0455292
- Marcel Meicler, Chebyshev solution of an inconsistent system of $n+1$ linear equations in $n$ unknowns in terms of its least squares solution, SIAM Rev. 10 (1968), 373–375. MR 232783, DOI 10.1137/1010064
- David Moursund, Chebyshev solution of $n+1$ linear equations in $n$ unknowns, J. Assoc. Comput. Mach. 12 (1965), 383–387. MR 182139, DOI 10.1145/321281.321289
- R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc. 51 (1955), 406–413. MR 69793
Additional Information
- © Copyright 1969 American Mathematical Society
- Journal: Math. Comp. 23 (1969), 813-817
- MSC: Primary 65.30
- DOI: https://doi.org/10.1090/S0025-5718-1969-0258251-6
- MathSciNet review: 0258251