A difficulty in Williams’ algorithm for interpolating rationals

Dunham, Charles B.

doi:10.1090/S0025-5718-1975-0371014-9

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

A difficulty in Williams’ algorithm for interpolating rationals
HTML articles powered by AMS MathViewer

by Charles B. Dunham PDF

Math. Comp. 29 (1975), 552-553 Request permission

Abstract:

J. Williams has developed a theory and an algorithm for best Chebyshev approximation of decay-type functions by an oscillation factor times a negative power of a linear form (in particular a polynomial). It is shown that the levelling equations of the algorithm may not have an admissible solution.

References

Richard B. Barrar and Henry L. Loeb, On the Remez algorithm for non-linear families, Numer. Math. 15 (1970), 382–391. MR 267724, DOI 10.1007/BF02165509
Jack Williams, Numerical Chebyshev approximation by interpolating rationals, Math. Comp. 26 (1972), 199–206. MR 373230, DOI 10.1090/S0025-5718-1972-0373230-6