An Algorithm for the Generalized Matrix Eigenvalue Problem Ax = Lambda Bx

Abstract

A new method, called the QZ algorithm, is presented for the solution of the matrix eigenvalue problem Ax = lambda Bx with general square matrices A and B. Particular attention is paid to the degeneracies which result when B is singular. No inversions of B or its submatrices are used. The algorithm is a generalization of the QR algorithm, and reduces to it when B = I. A FORTRAN program and some illustrative examples are included.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1971
Accession Number
AD0746896

Entities

People

  • C. B. Moler
  • G. W. Stewart

Organizations

  • University of Michigan

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Computations
  • Computer Programs
  • Computer Science
  • Computers
  • Coordinate Systems
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Iterations
  • Linear Accelerators
  • Mathematics
  • Numbers
  • Numerical Analysis
  • Procedures (Computers)
  • Square Roots
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Linear Algebra