Accession Number : ADA192996

Title :   Leapfrog Variants of Iterative Methods for Linear Algebraic Equations.

Descriptive Note : Final rept.,

Corporate Author : INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA

Personal Author(s) : Saylor, Paul E

PDF Url : ADA192996

Report Date : Jan 1988

Pagination or Media Count : 62

Abstract : Two iterative methods are considered, Richardson's method and a general second order method. For both methods, a variant of the method is derived for which only even numbered iterates are computed. The variant is called a leapfrog method. Comparisons between the conventional form of the methods and the leapfrog form are made under the assumption that the number of unknowns is large. In the case of Richardson's method, it is possible to express the final iterate in terms of only the initial approximation, a variant of the iteration called the grand-leap method. In the case of the grand-leap variant, a set of parameters is required. An algorithm is presented to compute these parameters that is related to algorithms to complete the weights and abscissas for Gaussian quadrature. General algorithms to implement the leapfrog and grand-leap methods are presented. Algorithms for the important special case of the Chebyshev method are also given.

Descriptors :   *ITERATIONS, *VARIATIONS, ALGORITHMS, GAUSSIAN QUADRATURE, LINEAR ALGEBRAIC EQUATIONS, PARAMETERS

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE