RATE OF CONVERGENCE PROOFS OF THE METHOD FOR FINDING ROOTS OF POLYNOMIALS (OR EIGENVALUES OF MATRICES) BY THE POWER AND INVERSE POWER METHODS.
Abstract
Generally known proofs of the convergence of the power method and the inverse power method for finding eigenvalues of a matrix are presented in some detail. The power method is shown to converge geometrically for diagonalizable matrices and proportional to 1/r for nondiagonalizable matrices, where r is the iteration number. The inverse power method is shown to converge at least quadratically for diagonalizable matrices. No rigorous proof of convergence for the inverse power method for nondiagonalizable matrices is given, but several comments are made and an expression for the rate of convergence is presented, along with experimental results. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1969
- Accession Number
- AD0707331
Entities
People
- L. W. Ehrlich
Organizations
- Johns Hopkins University Applied Physics Laboratory