Accession Number:

ADA151491

Title:

The Matrix Sector Functions and their Applications to Systems Theory.

Descriptive Note:

Rept. for 1 Jul-31 Dec 84,

Corporate Author:

HOUSTON UNIV TX DEPT OF ELECTRICAL ENGINEERING

Personal Author(s):

• Shieh, L. S.
• Tsay, Y. T.
• Wang, C. T.

Report Date:

1984-09-01

Pagination or Media Count:

12.0

Abstract:

The paper presents a new matrix function, the matrix sector function of a square complex matrix A, and its applications to systems theory. Firstly, based on an irrational function of a complex variable, a scalar sector function is defined. Next, a fast algorithm is developed with the help of a circulant matrix for computing the scalar sector function of lambda. Then, the scaler sector function of lambda is extended to a matrix sector function, and to associated partitioned matrix sector functions of A. Finally, the applications of these matrix sector functions to the separation of matrix eigenvalues, the determination of A-invariant space, the block diagonalisation of a matrix, and the generalised block partial fraction expansion of a rational matrix are given. It is shown that the well-known matrix sign function of A is a special class of the newly developed matrix sector function of A. It is also shown that the Newton-Raphson type algorithm cannot, in general, be applied to determine the matrix sector function of A. Originator supplied keywords include Mathematical technique Approximation theory Eigenfunctions Linear systems.

Descriptors:

• *MATRIX THEORY
• ALGORITHMS
• APPROXIMATION(MATHEMATICS)
• EIGENVECTORS
• LINEAR SYSTEMS
• MATRIX DISPLAYS
• SCALAR FUNCTIONS

Subject Categories:

• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE