Accession Number:

ADA093568

Title:

Extremal Polynomials with Application to Richardson Iteration for Indefinite Linear Systems.

Descriptive Note:

Technical summary rept.,

Corporate Author:

WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s):

• DE Boor,Carl
• Rice,John R.

Report Date:

1980-08-01

Pagination or Media Count:

30.0

Abstract:

The application of Richardson iteration to a symmetric, but indefinite linear system requires certain parameters which can be determined from the zeros in the error of a certain best polynomial approximant on some set S known to contain the spectrum of the coefficient matrix. It is pointed out that this error can also be obtained as a multiple of the extremal polynomial for the linear functional p at p0, and this leads to an efficient Remes type algorithm for its determination. A program incorporating this algorithm for the case that S consists of two intervals bracketing zero is also given. Author

Descriptors:

• *LINEAR SYSTEMS
• *ITERATIONS
• *CHEBYSHEV POLYNOMIALS
• COMPUTER PROGRAMS
• COMPUTERIZED SIMULATION
• MATRICES(MATHEMATICS)
• GRAPHS
• FORTRAN
• APPROXIMATION(MATHEMATICS)
• LEAST SQUARES METHOD
• CONVERGENCE
• OPERATORS(MATHEMATICS)
• THEOREMS

Subject Categories:

• Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE