Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Linear Chebyshev approximation of complex-valued functions


Authors: I. Barrodale, L. M. Delves and J. C. Mason
Journal: Math. Comp. 32 (1978), 853-863
MSC: Primary 65D15; Secondary 41A50
DOI: https://doi.org/10.1090/S0025-5718-1978-0483298-X
MathSciNet review: 0483298
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This paper is concerned with Chebyshev approximation by linear functions to complex-valued data. The problem is nonlinear, and we present a convergent algorithm for its solution. We also pose a related linear problem which is simple to solve, and which produces approximations which are near-best in the Chebyshev sense within a factor of $ \sqrt 2 $. Some numerical examples are provided.


References [Enhancements On Off] (What's this?)

  • [1] I. BARRODALE & C. PHILLIPS, Algorithm 495--Solution of an Overdetermined System of Linear Equations in the Chebyshev Norm, ACM Trans. Math. Software, v. 1, 1975, pp. 264-270. MR 0373585 (51:9785)
  • [2] L. COLLATZ & W. WETTERLING, Optimization Problems, Springer-Verlag, Berlin and New York, 1975, pp. 278-280. MR 0377635 (51:13806)
  • [3] S. ELLACOTT & JACK WILLIAMS, "Linear Chebyshev approximation in the complex plane using Lawson's algorithm," Math. Comp., v. 30, 1976, pp. 35-44. MR 0400652 (53:4483)
  • [4] K. O. GEDDES & J. C. MASON, "Polynomial approximation by projections on the unit circle," SIAM J. Numer. Anal., v. 12, 1975, pp. 111-120. MR 0364977 (51:1230)
  • [5] P. E. GILL & W. MURRAY, Numerical Methods for Constrained Optimization, Academic Press, New York, 1974. MR 0395227 (52:16025)
  • [6] C. L. LAWSON, Contributions to the Theory of Linear Least Maximum Approximations, Thesis, Univ. of California, Los Angeles, 1961.
  • [7] G. G. LORENTZ, Approximation of Functions, Holt, Rinehart and Winston, New York,1966. MR 0213785 (35:4642)
  • [8] P. RABINOWITZ, "Mathematical programming and approximation," in Approximation Theory, A. Talbot (Editor), Academic Press, New York, 1970, pp. 217-231. MR 0267896 (42:2797)
  • [9] D. M. SIMMONS, Nonlinear Programming for Operations Research, Prentice-Hall, Englewood Cliffs, N. J., 1975, (Chapter 9).
  • [10] W. I. ZANGWILL, Nonlinear Programming, Prentice-Hall, Englewood Cliffs, N. J., 1969, (Chapter 14).
  • [11] S. I. ZUKHOVITSKIY & L. I. AVDEYEVA, Linear and Convex Programming, Saunders, Philadelphia, 1966, (Chapter 6). MR 0226936 (37:2522)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65D15, 41A50

Retrieve articles in all journals with MSC: 65D15, 41A50


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1978-0483298-X
Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society