Solutions of Certain Matrix Equations with Applications to Engineering Sciences.
Abstract
Solutions of certain matrix equations are presented in this thesis. Results of Mitra are used to extend current methods of obtaining a general form of the solution of the Liapunov equation. Solutions of the general linear matrix equation, including important special cases, are obtained under rather general conditions on the matrices. Necessary and sufficient conditions are established for the existence of a solution of AX = C where the elements of the matrices belong to the polynomial domain of the field of real numbers. Representations of solutions to the algebraic Riccati equation are given along with original techniques for computation of solutions and conditions for uniqueness. Sufficient conditions for the existence of the generalized nonlinear algebraic and differential Riccati equations are established. The classical Newton-Raphson method of finding zeros of functions of a single variable is extended to the case of finding zeros of functions of a matrix variable, including determining the inverse of a matrix. An extensive bibliography includes a comprehensive listing of articles which provide historical and developmental background on the matrix equations considered in this thesis. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1976
- Accession Number
- ADA032667
Entities
People
- James L. Leuthauser
Organizations
- Air Force Institute of Technology