Accession Number : AD0694464

Title :   THREE-STAGE VARIABLE-SHIFT ITERATIONS FOR THE SOLUTION OF POLYNOMIAL EQUATIONS WITH A POSTERIORI ERROR BOUNDS FOR THE ZEROS.

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CALIF DEPT OF COMPUTER SCIENCE

Personal Author(s) : Jenkins,Michael A. G.

Report Date : AUG 1969

Pagination or Media Count : 204

Abstract : Two new algorithms are introduced for solving polynomial equations and their implementation in ALGOL 60. An ALGOL 60 program is included for finding error bounds and improved approximations. The first zerofinding algorithm is a three-stage process for complex polynomials which is related to applying inverse iteration to the companion matrix. The three stages correspond to using inverse iteration with no shift, a fixed shift and a variable shift. A proof is included that the three stage algorithm always converges and that the third stage has a 'better than quadratic' rate of convergence. The second zerofinding algorithm is a related three-stage process for real polynomials which finds either linear or quadratic factors. The bound program finds individual bounds with an option for improving the approximations. Numerical tests indicate that the amount of work done by the zerofinding program is almost independent of the configuration of the zeros. (Author)

Descriptors :   (*COMPUTER PROGRAMMING, NUMERICAL ANALYSIS), (*NUMERICAL ANALYSIS, *POLYNOMIALS), PROGRAMMING LANGUAGES, APPROXIMATION(MATHEMATICS), ITERATIONS, COMPUTER PROGRAMS, ALGORITHMS, ERRORS, THEOREMS, THESES

Subject Categories : Theoretical Mathematics
      Computer Programming and Software

Distribution Statement : APPROVED FOR PUBLIC RELEASE