A note on an algorithm for interpolating rationals

Authors:
You Gun Huang and Jack Williams

Journal:
Math. Comp. **42** (1984), 111-113

MSC:
Primary 65D05; Secondary 41A20

MathSciNet review:
725987

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**[1]**Charles B. Dunham,*A difficulty in Williams’ algorithm for interpolating rationals*, Math. Comp.**29**(1975), 552–553. MR**0371014**, 10.1090/S0025-5718-1975-0371014-9**[2]**Darrell Schmidt,*An existence theorem for Chebyshev approximation by interpolating rationals*, J. Approx. Theory**27**(1979), no. 2, 146–152. MR**554005**, 10.1016/0021-9045(79)90116-3**[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**0355435**, 10.1090/S0025-5718-1974-0355435-5**[4]**Jack Williams,*Numerical Chebyshev approximation by interpolating rationals*, Math. Comp.**26**(1972), 199–206. MR**0373230**, 10.1090/S0025-5718-1972-0373230-6

Retrieve articles in *Mathematics of Computation*
with MSC:
65D05,
41A20

Retrieve articles in all journals with MSC: 65D05, 41A20

Additional Information

DOI:
http://dx.doi.org/10.1090/S0025-5718-1984-0725987-8

Article copyright:
© Copyright 1984
American Mathematical Society