Algorithms for Solvents and Spectral Factors of Matrix Polynomials

Abstract

A generalized Newton method, based on the contracted gradient of a matrix polynomial, is derived for solving the right (left) solvents and spectral factors of matrix polynomials. Two methods of selecting initial estimates for rapid convergence of the newly developed numerical method are proposed. Also, new algorithms for solving complete sets of the right (left) solvents and spectral factors without directly using the eigenvalues of matrix polynomials are derived. The proposed computer-aided method can be used to determine the spectral factorization of a matrix polynomial for optimal control, filtering and estimation problems.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1981
Accession Number
ADA115828

Entities

People

  • Leang S. Shieh
  • Norman P. Coleman
  • Yih T. Tsay

Organizations

  • University of Houston

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Complex Variables
  • Computations
  • Computers
  • Control Systems
  • Convergence
  • Differential Equations
  • Eigenvalues
  • Electrical Engineering
  • Engineering
  • Equations
  • Filtration
  • Functional Analysis
  • Mathematical Analysis
  • New York
  • Polynomials
  • Systems Science

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Calculus or Mathematical Analysis