On Randomized Lanczos Algorithms

Las Vegas algorithms that are based on Lanczos’s method for solving symmetric linear systems are presented and analyzed. These are compared to a similar randomized Lanczos algorithm that has been used for integer factorization, and to the (provably reliable) algorithm of Wiedemann. The analysis suggests that our Lanczos algorithms are preferable to several versions of Wiedemann’s method for computations over large fields, especially for certain symmetric matrix computations.

• Type: Conference
• Year: 1997
• Where: ISSAC
• Authors: Wayne Eberly, Erich Kaltofen
• Keywords: ISSAC 1997, Lanczos Algorithms, Lanczos’s Method, Mathematics, Similar Randomized Lanczos