block Lanczos algorithm

Matrices, moments and quadrature

Published in D F Griffiths, G A Watson, Numerical analysis 1993, 2020

It is easy to understand why we cannot directly obtain bounds with this block approach. We must use W = (e¿ e f) and the block Lanczos algorithm with ¾ = W. For the block Lanczos algorithm we multiply successively A with the Lanczos vectors. If Ais sparse, most of the components of these products are 0 for the first few iterates of the algorithm. Therefore, it is likely that at the beginning, the estimates that we will get for the non diagonal entries will be 0. This explains why we cannot directly obtain upper or lower bounds with Gauss, Gauss-Radau or Gauss-Lobatto. A way to avoiding this difficulty is to use W = (e¿ + t j e ¿) but this cannot be done since Xo ψ Iļ·

Linear Algebra on Parallel Structures Using Wiedemann Algorithm to Solve Discrete Logarithm Problem

View Article

Journal Information

Published in IETE Journal of Research, 2022

K S Spoorthi, R. Padmavathy, S K Pal, S Ravi Chandra

Lanczos proposed an iterative solution for solving a system of linear equations [23]. Lanczos algorithm was later developed into a parallelized version called the block Lanczos algorithm [22, 24]. Earlier Joux et al., used Lanczos method in linear algebra of FFS to solve the DLP.

block Lanczos algorithm

Explore chapters and articles related to this topic

Matrices, moments and quadrature

Linear Algebra on Parallel Structures Using Wiedemann Algorithm to Solve Discrete Logarithm Problem