Section: New Results

A Modified Block Lanczos Algorithm with Fewer Vectors

Participant : Emmanuel Thomé [contact] .

In the context of a book project entitled “Topics in Computational Number Theory inspired by Peter L. Montgomery” (edited by Joppe W. Bos and Arjen K. Lenstra), E. Thomé contributed a chapter on “the Block Lanczos algorithm” (owed to Peter L. Montgomery [35]). This was the occasion to rework and streamline the presentation of the block Lanczos algorithm. In fact, several new characteristics of the algorithm were obtained in this process: a version adapted to homogeneous systems, an improvement on the memory footprint of the algorithm, and a heuristic justification for the success probability of the algorithm. While the collated book is still not published yet (publication is expected in 2017), the chapter is published in preprint form as [14].