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.

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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

Tags

Communities of Interest

  • Biomedical
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Air Force
  • Algebra
  • Classification
  • Coefficients
  • Complex Numbers
  • Computer Programs
  • Computers
  • Differential Equations
  • Equations
  • Mathematics
  • Numbers
  • Polynomials
  • Real Numbers
  • Reasoning
  • Riccati Equation
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Computational Modeling and Simulation
  • Linear Algebra