A note on an algorithm for interpolating rationals
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- by You Gun Huang and Jack Williams PDF
- Math. Comp. 42 (1984), 111-113 Request permission
Abstract:
This note considers an aspect of the simultaneous exchange algorithm for Chebyshev approximation by interpolating rationals. An example has been given by Dunham claiming to show that this algorithm may fail to produce an interpolating rational approximant. In this note we show that his example cannot occur as a step of the exchange algorithm. A second example is given where Dunham’s objection to the algorithm is valid.References
- Charles B. Dunham, A difficulty in Williams’ algorithm for interpolating rationals, Math. Comp. 29 (1975), 552–553. MR 371014, DOI 10.1090/S0025-5718-1975-0371014-9
- Darrell Schmidt, An existence theorem for Chebyshev approximation by interpolating rationals, J. Approx. Theory 27 (1979), no. 2, 146–152. MR 554005, DOI 10.1016/0021-9045(79)90116-3
- G. D. Taylor and J. Williams, Existence questions for the problem of Chebyshev approximation by interpolating rationals, Math. Comp. 28 (1974), 1097–1103. MR 355435, DOI 10.1090/S0025-5718-1974-0355435-5
- Jack Williams, Numerical Chebyshev approximation by interpolating rationals, Math. Comp. 26 (1972), 199–206. MR 373230, DOI 10.1090/S0025-5718-1972-0373230-6
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Math. Comp. 42 (1984), 111-113
- MSC: Primary 65D05; Secondary 41A20
- DOI: https://doi.org/10.1090/S0025-5718-1984-0725987-8
- MathSciNet review: 725987