Accession Number:

AD0773392

Title:

The Laurent-Pade Table,

Descriptive Note:

Corporate Author:

CALIFORNIA UNIV SAN DIEGO LA JOLLA DEPT OF MATHEMATICS

Personal Author(s):

Report Date:

1973-12-01

Pagination or Media Count:

22.0

Abstract:

The Pade table of a formal power series is a natural extension of the Taylor series to rational functions. It has connections with many areas, but is not as useful as one might think for the practical approximation of functions. The paper extends the concept to doubly infinite formal Laurent series with a view toward approximation of functions on intervals. The earlier approach of Maehly is mentioned. Basic existence, uniqueness and algorithmic results are established for the Laurent-Pade table. Connections with moments and orthogonal polynomials are indicated and used to establish a sharp convergence theorem for the class of Chebyshev transforms. Finally, numerical experience with near best uniform rational approximation to e sup x on -1, 1 is related. Author

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE