Algorithms for computing nth roots and the matrix sector function of nonsingular complex matrices

Author

Hasan, Mohammed A. ; Hasan, Jawad A K

Author_Institution

Dept. of Electr. & Comput. Eng., Minnesota Univ., Duluth, MN, USA

Volume

2

fYear

2000

fDate

2000

Firstpage

1390

Abstract

New fast convergent methods for computing the principal nth roots, and matrix sector functions of nonsingular complex matrices are developed. The main features of these methods in addition to higher order convergence are (1) they are power-like methods and thus they are stable and self-correcting, (2) they are globally convergent in that they converge from a broad set of initial conditions, and (3) they are less sensitive to sector boundary. Additionally the techniques of the paper allow for computing a set of projectors onto some of the subeigenspaces which can be used to compute the number of eigenvalues in a given sector and to compute more nth roots of a given matrix. Several examples are also included to illustrate the performance of the proposed algorithms

Keywords

convergence; eigenvalues and eigenfunctions; functions; matrix algebra; polynomials; fast convergent methods; globally convergent methods; higher order convergence; matrix sector function; nonsingular complex matrices; power-like methods; principal nth roots; subeigenspaces; Control theory; Eigenvalues and eigenfunctions; Null space; Polynomials; Power engineering and energy; Power engineering computing; Riccati equations;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 2000. Proceedings of the 2000

Conference_Location

Chicago, IL

ISSN

0743-1619

Print_ISBN

0-7803-5519-9

Type

conf

DOI

10.1109/ACC.2000.876729

Filename

876729