## Linear Chebyshev approximation of complex-valued functions

HTML articles powered by AMS MathViewer

- by I. Barrodale, L. M. Delves and J. C. Mason PDF
- Math. Comp.
**32**(1978), 853-863 Request permission

## 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

- I. Barrodale and C. Phillips,
*An improved algorithm for discrete Chebyshev linear approximation*, Proceedings of the Fourth Manitoba Conference on Numerical Mathematics (Winnipeg, Man., 1974) Congr. Numer., No. XII, Utilitas Math., Winnipeg, Man., 1975, pp. 177–190. MR**0373585** - L. Collatz and W. Wetterling,
*Optimization problems*, Applied Mathematical Sciences, Vol. 17, Springer-Verlag, New York-Heidelberg, 1975. Translated from the German by P. Wadsack. MR**0377635** - S. Ellacott and Jack Williams,
*Linear Chebyshev approximation in the complex plane using Lawson’s algorithm*, Math. Comput.**30**(1976), no. 133, 35–44. MR**0400652**, DOI 10.1090/S0025-5718-1976-0400652-0 - K. O. Geddes and J. C. Mason,
*Polynomial approximation by projections on the unit circle*, SIAM J. Numer. Anal.**12**(1975), 111–120. MR**364977**, DOI 10.1137/0712011 *Numerical methods for constrained optimization*, Academic Press, London-New York, 1974. Edited by P. E. Gill and W. Murray. MR**0395227**
C. L. LAWSON, - G. G. Lorentz,
*Approximation of functions*, Holt, Rinehart and Winston, New York-Chicago, Ill.-Toronto, Ont., 1966. MR**0213785** - P. Rabinowitz,
*Mathematical programming and approximation*, Approximation Theory (Proc. Sympos., Lancaster, 1969) Academic Press, London, 1970, pp. 217–231. MR**0267896**
D. M. SIMMONS, - S. I. Zukhovitskiy and L. I. Avdeyeva,
*Linear and convex programming*, W. B. Saunders Co., Philadelphia, Pa.-London, 1966. Translated from the Russian by Scripta Technica, Inc; Edited by Bernard R. Gelbaum. MR**0226936**

*Contributions to the Theory of Linear Least Maximum Approximations*, Thesis, Univ. of California, Los Angeles, 1961.

*Nonlinear Programming for Operations Research*, Prentice-Hall, Englewood Cliffs, N. J., 1975, (Chapter 9). W. I. ZANGWILL,

*Nonlinear Programming*, Prentice-Hall, Englewood Cliffs, N. J., 1969, (Chapter 14).

## Additional Information

- © Copyright 1978 American Mathematical Society
- 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