|
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
MathSciNet review:
0402355
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
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
(40 #6137)
- [2]
Charles
B. Dunham, Chebyshev approximation with respect to a vanishing
weight function, J. Approximation Theory 12 (1974),
305–306. MR 0355438
(50 #7912)
- [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
(39 #5989)
- [7]
Jack
Williams, Numerical Chebyshev approximation by
interpolating rationals, Math. Comp. 26 (1972), 199–206.
MR
0373230 (51 #9431), http://dx.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
(50 #7909), http://dx.doi.org/10.1090/S0025-5718-1974-0355435-5
- [1]
- C. B. DUNHAM, "Chebyshev approximation with respect to a weight function," J. Approximation Theory, v. 2, 1969, pp. 223-232. MR 40 #6137. MR 0252922 (40:6137)
- [2]
- C. B. DUNHAM, "Chebyshev approximation with respect to a vanishing weight function," J. Approximation Theory, v. 12, 1974, pp. 305-306. MR 0355438 (50:7912)
- [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]
- J. R. RICE, The Approximation of Functions. Vol. 2: Nonlinear and Multivariate Theory, Addison-Wesley, Reading, Mass., 1969. MR 39 #5989. MR 0244675 (39:5989)
- [7]
- J. WILLIAMS, "Numerical Chebyshev approximation by interpolating rationals," Math. Comp., v. 26, 1972, pp. 199-206. MR 0373230 (51:9431)
- [8]
- G. D. TAYLOR & J. WILLIAMS, "Existence questions for the problem of Chebyshev approximation by interpolating rationals," Math. Comp., v. 28, 1974, pp. 1097-1103. MR 0355435 (50:7909)
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
41A50
Retrieve articles in all journals
with MSC:
41A50
Additional Information
DOI:
http://dx.doi.org/10.1090/S0025-5718-1976-0402355-5
PII:
S 0025-5718(1976)0402355-5
Article copyright:
© Copyright 1976 American Mathematical Society
|
