A Generalization of the LR Algorithm to Solve AX = lambda BX

Abstract

In the paper, the author presents and analyzes an algorithm for finding x and lambda such that Ax = lambda Bx, where A and B are n x n matrices. The algorithm does not require matrix inversion, and may be used when either or both matrices are singular. The method is a generalization of Rutishauser's LR method for the standard eigenvalue problem Ax = lambda x and closely resembles the QZ algorithm given by Moler and Steward for the generalized problem given above. Unlike the QZ algorithm, which uses orthogonal transformations, the method, the LZ algorithm, uses elementary transformations. When either A or B is complex, the method should be more efficient.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1972
Accession Number
AD0745022

Entities

People

  • Linda Kaufman

Organizations

  • Stanford University

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Arithmetic
  • Computer Science
  • Computers
  • Convergence
  • Coordinate Systems
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Iterations
  • Numbers
  • Numerical Analysis
  • Precision
  • Square Roots
  • Theorems
  • United States
  • United States Government

Fields of Study

  • Mathematics

Readers

  • Linear Algebra