How to Make the Lanczos Algorithm Converge Slowly.
CALIFORNIA UNIV BERKELEY ELECTRONICS RESEARCH LAB
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The Paige style Lanczos algorithm is an iterative method for finding a few eigenvalues of large sparse symmetric matrices. Some beautiful relationships among the elements of the eigenvectors of a symmetric tridiagonal matrix are used to derive a perverse starting vector which delays convergence as long as possible. Why such slow convergence is never seen in practice is also examined. Author
- Theoretical Mathematics