Accession Number : AD0707331

Title :   RATE OF CONVERGENCE PROOFS OF THE METHOD FOR FINDING ROOTS OF POLYNOMIALS (OR EIGENVALUES OF MATRICES) BY THE POWER AND INVERSE POWER METHODS.

Descriptive Note : Technical memo.,

Corporate Author : JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB

Personal Author(s) : Ehrlich,L. W.

Report Date : DEC 1969

Pagination or Media Count : 52

Abstract : Generally known proofs of the convergence of the power method and the inverse power method for finding eigenvalues of a matrix are presented in some detail. The power method is shown to converge geometrically for diagonalizable matrices and proportional to 1/r for nondiagonalizable matrices, where r is the iteration number. The inverse power method is shown to converge at least quadratically for diagonalizable matrices. No rigorous proof of convergence for the inverse power method for nondiagonalizable matrices is given, but several comments are made and an expression for the rate of convergence is presented, along with experimental results. (Author)

Descriptors :   (*MATRICES(MATHEMATICS), NUMERICAL ANALYSIS), (*POLYNOMIALS, *NUMERICAL ANALYSIS), ITERATIONS, CONVERGENCE

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE