Rational approximation with a vanishing weight function and with a fixed value at zero

Author:
Charles B. Dunham

Journal:
Math. Comp. **30** (1976), 45-47

MSC:
Primary 41A50

DOI:
https://doi.org/10.1090/S0025-5718-1976-0402355-5

MathSciNet review:
0402355

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Abstract: Chebyshev approximation by ordinary rational functions with respect to a vanishing weight function is considered. A best approximation is characterized by alternation and is unique but may not exist. The problem arises in Kuki's technique for rational approximation with interpolation at zero and with Williams' interpolating rationals.

**[1]**Charles B. Dunham,*Chebyshev aproximation with respect to a weight function*, J. Approximation Theory**2**(1969), 223–232. MR**0252922****[2]**Charles B. Dunham,*Chebyshev approximation with respect to a vanishing weight function*, J. Approximation Theory**12**(1974), 305–306. MR**0355438****[3]***IBM System*/360*FORTRAN*IV*Library Subprograms*, 5th ed., October 1968.**[4]**H. KUKI,*Mathematical Functions*, University of Chicago Computation Center Report, 1966.**[5]**H. KUKI & J. ASCOLY, "FORTRAN extended-precision library,"*IBM Systems J.*, v. 10, 1971, pp. 39-61.**[6]**John R. Rice,*The approximation of functions. Vol. 2: Nonlinear and multivariate theory*, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. MR**0244675****[7]**Jack Williams,*Numerical Chebyshev approximation by interpolating rationals*, Math. Comp.**26**(1972), 199–206. MR**0373230**, https://doi.org/10.1090/S0025-5718-1972-0373230-6**[8]**G. D. Taylor and J. Williams,*Existence questions for the problem of Chebyshev approximation by interpolating rationals*, Math. Comp.**28**(1974), 1097–1103. MR**0355435**, https://doi.org/10.1090/S0025-5718-1974-0355435-5

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DOI:
https://doi.org/10.1090/S0025-5718-1976-0402355-5

Article copyright:
© Copyright 1976
American Mathematical Society