Solutions of Nonlinear Matrix Equations.
Abstract
This thesis seeks the solutions to a system of equations (equalities) in n variables by expressing the system in matrix algebraic form. Properties of the solutions to the ensuing matrix equation are investigated using similarity transformations. The three types of matrix equations to be studied are: the linear equation - AX = b; the Lypunov equation - AX - XB = C; the second-order Riccati equation - XDX + AX + XB + C = 0; and the third-order Riccati equation = XAXBX + XCX + DX + XE + F = 0. Because adding and multiplying matrices (having multivariate polynomial entries) is tedious in practice, an interactive BASIC program is presented in the appendix. This program, which can be used on a personal computer, permits the user to perform operations on matrices having multivariate polynomial entries.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1985
- Accession Number
- ADA163841
Entities
People
- Bruce W. Colletti
Organizations
- Air Force Institute of Technology