On the Quadratic Convergence of the Falk–Langemeyer Method
- 1 January 1991
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Matrix Analysis and Applications
- Vol. 12 (1) , 84-114
- https://doi.org/10.1137/0612008
Abstract
The Falk–Langemeyer method for solving a real definite generalized eigenvalue problem, $Ax = \lambda Bx$, $x \ne 0$, is proved to be quadratically convergent under arbitrary cyclic pivot strategy if the eigenvalues of the problem are simple. The term “quadratically convergent” means roughly that the sum of squares of the off-diagonal elements of matrices from the sequence of matrix pairs generated by the method tends to zero quadratically per cycle.
Keywords
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