A fast algorithm for linear complex chebyshev approximations

Mathematics of Computation

Volumn 51, Issue 184, 1988, Pages 721-739

  Peter Tang, Ping Tak ^a  

^a ARGONNE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001396701     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-1988-0935074-5     Document Type: Article

References (28)

1. I. BARRODALE, L. M. DELVES & J. C. MASON, "Linear Chebyshev approximation of complex-valued functions, " Math. Comp., v. 32, 1978,. 853-863.
2. H. P. BLATT, "On strong uniqueness in linear complex Chebyshev approximation, ". J. Approx. Theory, v. 41, 1984,. 159-169.
3. E. W. CHENEY, Introduction to Approximation Theory, 2nd ed., Chelsea, New York, 1986.
4. C. B. DUNHAM & J. WILLIAMS, "Rate of convergence of discretization in Chebyshev approximation, " Math. Comp., v. 37, 1981,. 135-139.
5. S. W. ELLACOTT & J. WILLIAMS, "Linear Chebyshev approximation in the complex plane using Lawson's algorithm, " Math. Comp., v. 30, 1976,. 35-44.
6. H. C. ELMAN & R. L. STREIT, Polynomial Iteration for Nonsymmetric Indefinite Linear Systems, Research report YALEU/DCS/RR-380, Department of Computer Science, Yale University, New Haven, Conn., March 1985.
7. B. FRANCIS, J. W. HELTON & G. ZAMES, "#°°-optimal feedback controllers for linear multivariable systems, " IEEE Trans. Automat. Control, v. 29, 1984,. 888-900.
8. W. Gautschi, "Efficient computation of the complex error function, " SIAM J. Numer. Anal., v. 7, 1970,. 187-198.
9. K. GLASHOFF ¿i K. ROLEFF, "A new method for Chebyshev approximation of complexvalued functions, " Math. Comp., v. 36, 1981,. 233-239.
10. M. H. GUTKNECHT, "Non-strong uniqueness in real and complex Chebyshev approximation, " J. Approx. Theory, v. 23, 1978,. 204-213.
11. M. HARTMANN & G. OPFER, "Uniform approximation as a numerical tool for constructing conformai maps, " J. Comput. Appl. Math., v. 14, 1986,. 193-206.
12. J. W. HELTON, "Worst case analysis in the frequency domain: An H°° approach for control, " IEEE Trans. Automat. Control, v. AC-30, 1985,. 1192-1201.
13. A. K. Huí, B. H. ARMSTRONG & A. A. WRAY, "Rapid computation of the Voigt and complex error functions, " J. Quant. Spectrosc. Radiât. Transfer, v. 19, 1978,. 509-516.
14. J. HUMLÍCEK, "Optimized computation of the Voigt and complex probability functions, " J. Quant. Spectrosc. Radiât. Transfer, v. 27, 1982,. 437-444.
15. W. KAHAN, Lecture Notes on Superlinear Convergence of a Remes Algorithm, Class Notes for Computer Science 274, University of California at Berkeley, April 1981.
16. P. LAURENT & C. Carasso, "An algorithm of successive minimization in convex programming, " RAIRO Anal Numér., v. 12, 1978,. 377-400.
17. C. L. LAWSON, Contributions to the Theory of Linear Least Maximum Approximations, Ph.D. thesis, University of California at Los Angeles, 1961.
18. D. G. LUENBERGER, Linear and Nonlinear Programming, 2nd ed., Addison-Wesley, Reading, Mass., 1984.
19. G. OPFER, "An algorithm for the construction of best approximation based on Kolmogorov's criterion, " J. Approx. Theory, v. 23, 1978,. 299-317.
20. G. OPFER, "New extremal properties for constructing conformai mappings, " Numer. Math., v. 32, 1979,. 423-429.
21. M. J. D. POWELL, Approximation Theory and Methods, Cambridge Univ. Press, Cambridge, 1981.
22. L. Reichel, "On polynomial approximation in the complex plane with application to conformal mapping, " Math. Comp., v. 44, 1985,. 425-433.
23. T. J. RIVLIN & H. S. SHAPIRO, "A unified approach to certain problems of approximation and minimization, " J. Soc. Indust. Appl. Math., v. 9, 1961,. 670-699.
24. R. L. STREIT & A. H. NUTTALL, "A general Chebyshev complex function approximation procedure and an application to beamforming, " J. Acoust. Soc. Amer., v. 72, 1982,. 181-190.
25. P. T. P. TANG, Chebyshev Approximation on the Complex Plane, Ph.D. thesis, Department of Mathematics, University of California at Berkeley, May 1987.
26. L. N. TREFETHEN, "Near circularity of the error curve in complex Chebyshev approximation, " J. Approx. Theory, v. 31, 1981,. 344-366.
27. L. VEIDINGER, "On the numerical determination of the best approximation in the Chebyshev sense, " Numer. Math., v. 2, 1960,. 99-105.
28. J. WILLIAMS, "Numerical Chebyshev approximation in the complex plane, " SIAM J. Numer. Anal., v. 9, 1972,. 638-649.