RATE OF CONVERGENCE PROOFS OF THE METHOD FOR FINDING ROOTS OF POLYNOMIALS (OR EIGENVALUES OF MATRICES) BY THE POWER AND INVERSE POWER METHODS.
JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB
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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 1r 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
- Theoretical Mathematics