Accession Number:

AD0770125

Title:

On the Convergence of an Algorithm for Rational Chebyshev Approximation.

Descriptive Note:

Master's thesis,

Corporate Author:

NAVAL POSTGRADUATE SCHOOL MONTEREY CALIF

Personal Author(s):

• Franke,Richard

Report Date:

1973-11-01

Pagination or Media Count:

19.0

Abstract:

An algorithm for rational Chebyshev approximation based on computing the zeros of the error curve was investigated. At each iteration the proposed zeros are corrected by changing them toward the abscissa of the adjacent extreme of largest magnitude. The algorithm is formulated as a numerical solution of a certain system of ordinary differential equations. Convergence is obtained by showing the system is asymptotically stable at the zeros of the best approximation. With an adequate initial guess, the algorithm has never failed for functions which have a standard error curve. Author

Descriptors:

• *RATIONAL FUNCTIONS
• *APPROXIMATION(MATHEMATICS)
• INTERPOLATION
• CONVERGENCE
• ALGORITHMS
• THEOREMS

Subject Categories:

• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE