A new method for Chebyshev approximation of complex-valued functions
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- by K. Glashoff and K. Roleff PDF
- Math. Comp. 36 (1981), 233-239 Request permission
Abstract:
In this paper we are concerned with a formulation of the Chebyshev approximation problem in the complex plane as a problem of linear optimization in the presence of infinitely many constraints. It is shown that there exist stable and fast algorithms for the solution of optimization problems of this type. Some numerical examples are presented.References
- D. O. Andreassen and G. A. Watson, Linear Chebyshev approximation without Chebyshev sets, Nordisk Tidskr. Informationsbehandling (BIT) 16 (1976), no. 4, 349–362. MR 451625, DOI 10.1007/bf01932717
- I. Barrodale, L. M. Delves, and J. C. Mason, Linear Chebyshev approximation of complex-valued functions, Math. Comp. 32 (1978), no. 143, 853–863. MR 483298, DOI 10.1090/S0025-5718-1978-0483298-X R. H. Bartels & G. H. Golub, "The simplex method of linear programming using LU-decompositions," Comm. ACM, v. 12, 1969, pp. 266-268. C. Carasso, L’Algorithme d’Echange en Optimisation Convexe, These, Grenoble, 1973.
- A. Charnes, W. W. Cooper, and K. Kortanek, Duality, Haar programs, and finite sequence spaces, Proc. Nat. Acad. Sci. U.S.A. 48 (1962), 783–786. MR 186393, DOI 10.1073/pnas.48.5.783
- S. Ellacott and Jack Williams, Rational Chebyshev approximation in the complex plane, SIAM J. Numer. Anal. 13 (1976), no. 3, 310–323. MR 413449, DOI 10.1137/0713028 K. Fahlander, Computer Programs for Semi-Infinite Optimization, TRITA-NA-7312, Department of Numerical Analysis, Royal Institute of Technology, S-10044, Stockholm 70, Sweden, 1973. K. Glashoff & S. Å. Gustafson, Einführung in die lineare Optimierung, Wissenschaftliche Buchgesellschaft, Darmstadt, 1978.
- S.-Ȧ. Gustafson, On the computational solution of a class of generalized moment problems, SIAM J. Numer. Anal. 7 (1970), 343–357. MR 270536, DOI 10.1137/0707026 S. Å. Gustafson, "Nonlinear system in semi-infinite programming," in Numerical Solution of Nonlinear Algebraic Systems (G. B. Byrnes & C. A. Hall, Eds.), Academic Press, New York, 1973, pp. 63-99.
- K.-H. Hoffmann and A. Klostermair, A semi-infinite linear programming procedure and applications to approximation problems in optimal control, Approximation theory, II (Proc. Internat. Sympos., Univ. Texas, Austin, Tex., 1976) Academic Press, New York, 1976, pp. 379–389. MR 0434406
- W. Krabs and G. Opfer, Eine Methode zur Lösung des komplexen Approximationsproblems mit einer Anwendung auf konforme Abbildungen, Z. Angew. Math. Mech. 55 (1975), no. 4, T208–T211 (German). MR 407495
- Gerhard Opfer, An algorithm for the construction of best approximations based on Kolmogorov’s criterion, J. Approx. Theory 23 (1978), no. 4, 299–317 (English, with German summary). MR 509560, DOI 10.1016/0021-9045(78)90082-5
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Math. Comp. 36 (1981), 233-239
- MSC: Primary 65D15; Secondary 30E10, 90C30
- DOI: https://doi.org/10.1090/S0025-5718-1981-0595055-4
- MathSciNet review: 595055