Uniform rational approximation on large data sets Journal Article uri icon

Overview

abstract

  • AbstractWe report on a very effective program for uniform approximation of functions (or discrete data) by generalized rational functions of any number of variables over point sets so large that conventional methods are inapplicable. The points need not be arranged in a regular pattern, but if they are, the number of points is normally limited only by the computer time available. The program extends the differential correction algorithm discussed in an earlier article in this journal by combining it with a first Remes‐type exchange procedure, while retaining the flexibility and robustness of differential correction. Furthermore, this algorithm is guaranteed to converge in theory. Testing has shown that, even when the point set is small enough for differential correction to be applied directly, this algorithm is usually faster. We discuss the algorithm and program along with several numerical examples, one of which involves more than three million data points. A FORTRAN listing with illustrative output can be obtained from the first author.

publication date

  • October 1, 1982

has restriction

  • closed

Date in CU Experts

  • September 17, 2013 7:59 AM

Full Author List

  • Kaufman EH; McCormick SF; Taylor GD

author count

  • 3

Other Profiles

International Standard Serial Number (ISSN)

  • 0029-5981

Electronic International Standard Serial Number (EISSN)

  • 1097-0207

Additional Document Info

start page

  • 1569

end page

  • 1575

volume

  • 18

issue

  • 10