An Algorithmic Approach for Reducing Kinematically Similar Differential Systems.

Abstract

Methods of reducing linear homogeneous differential matrix equations of the form X= A(t)X by kinematically similar transformations are presented in this thesis. Classical equivalence and similarity relationships between matrices with elements belonging to the polynomial domain with coefficients belonging to the field of real numbers are obtained which give necessary and sufficient conditions for the existence of solutions to certain polynomial equations. Block reduction techniques using kinematically similar transformations lead to a discussion of iterative and non-iterative solution methods for the Liapunov matrix equation, Liapunov differential matrix equation, Riccati matrix equation, and the Riccati differential matrix equation. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1977
Accession Number
ADA047781

Entities

People

  • Kevin Dolan

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • Biomedical
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Computations
  • Computers
  • Differential Equations
  • Eigenvalues
  • Equations
  • Linear Algebraic Equations
  • Linear Differential Equations
  • Numbers
  • Polynomials
  • Real Numbers
  • Real Variables
  • Riccati Equation
  • Sequences
  • Square Roots
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Linear Algebra