New Gradient Techniques for Traces of Functions of Rectangular Matrices and Their Pseudo-Inverses,

Abstract

The generalized inverse is of increasing importance for estimation and optimization in modern systems theory, because it both simplifies many problems and reveals underlying structures of theoretical importance. Optimization, using the gradient of the trace of products of matrix valued functions, including the generalized inverse, are presented in a novel state-space setting. A number of functions of such products of matrices, including general formulas, are derived for the first time to our knowledge. Tables of a number of them are given with some applications in the fields of estimation and optimization. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1977
Accession Number
ADA044808

Entities

People

  • James S. Pappas.
  • Oren N. Dalton

Tags

Communities of Interest

  • Energy and Power Technologies
  • Weapons Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Bessel Functions
  • Computations
  • Equations
  • Filters
  • Filtration
  • Kalman Filtering
  • Kalman Filters
  • Mathematical Filters
  • Matrix Theory
  • Numbers
  • Optimization
  • Power Series
  • Random Variables
  • Real Numbers
  • Riccati Equation
  • Test And Evaluation

Readers

  • Linear Algebra
  • Mathematical Modeling and Probability Theory.
  • Theoretical Analysis.

Technology Areas

  • Space