Accession Number : AD0650627

Title :   GRAEFFE'S METHOD FOR EIGENVALUES.

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CALIF DEPT OF COMPUTER SCIENCE

Personal Author(s) : Polya,G.

Report Date : 24 APR 1967

Pagination or Media Count : 13

Abstract : Let an entire function F(z) of finite genus have infinitely many zeros which are all positive, and take real values for real z. Then it is shown how to give two-sided bounds for all the zeros of F in terms of the coefficients of the power series of F, and of coefficients obtained by Graeffe's algorithm applied to F. A simple numerical illustration is given for a Bessel function.

Descriptors :   (*POWER SERIES, ALGORITHMS), (*BESSEL FUNCTIONS, CONVERGENCE), POLYNOMIALS, SEQUENCES(MATHEMATICS), INEQUALITIES, THEOREMS, DETERMINANTS(MATHEMATICS)

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE