Block Lanczos Techniques for Accelerating the Block Cimmino Method

1995 ◽  
Vol 16 (6) ◽  
pp. 1478-1511 ◽  
Author(s):  
Mario Arioli ◽  
Iain S. Duff ◽  
Daniel Ruiz ◽  
Miloud Sadkane
Keyword(s):  
Block Lanczos

The extended nonsymmetric block Lanczos methods for solving large-scale differential Lyapunov equations

2021 ◽  
Vol 8 (3) ◽  
pp. 526-536
Author(s):  
L. Sadek ◽  
◽  
H. Talibi Alaoui ◽  
Keyword(s):  
Matrix Equation ◽  
Large Scale ◽  
Krylov Subspace ◽  
Low Rank ◽  
Lyapunov Equations ◽  
Lanczos Algorithm ◽  
Lyapunov Matrix ◽  
Block Lanczos ◽  
Low Dimensional ◽  
Differential Lyapunov Equations

In this paper, we present a new approach for solving large-scale differential Lyapunov equations. The proposed approach is based on projection of the initial problem onto an extended block Krylov subspace by using extended nonsymmetric block Lanczos algorithm then, we get a low-dimensional differential Lyapunov matrix equation. The latter differential matrix equation is solved by the Backward Differentiation Formula method (BDF) or Rosenbrock method (ROS), the obtained solution allows to build a low-rank approximate solution of the original problem. Moreover, we also give some theoretical results. The numerical results demonstrate the performance of our approach.

A Block Lanczos Method for the CDT Subproblem

2019 ◽  
Vol 37 (2) ◽  
pp. 240-260
Author(s):  
Liqiang Song and Weihong Yang
Keyword(s):  
Lanczos Method ◽  
Block Lanczos ◽  
Block Lanczos Method

An Out-of-Core Eigen-Solver with OpenMP Parallel Scheme for Large Spare Damped System

2019 ◽  
Vol 16 (07) ◽  
pp. 1950038 ◽  
Author(s):  
S. H. Ju ◽  
H. H. Hsu
Keyword(s):  
Large Scale ◽  
Block Size ◽  
Lanczos Method ◽  
Preconditioned Conjugate Gradient ◽  
Damped System ◽  
Parallel Scheme ◽  
Complex Eigenvalues ◽  
Lanczos Iteration ◽  
Block Lanczos ◽  
Block Lanczos Method

An out-of-core block Lanczos method with the OpenMP parallel scheme was developed to solve large spare damped eigenproblems. The symmetric generalized eigenproblem is first solved using the block Lanczos method with the preconditioned conjugate gradient (PCG) method, and the condensed damped eigenproblem is then solved to obtain the complex eigenvalues. Since the PCG solvers and out-of-core schemes are used, a large-scale eigenproblem can be solved using minimal computer memory. The out-of-core arrays only need to be read once in each Lanczos iteration, so the proposed method requires little extra CPU time. In addition, the second-level OpenMP parallel computation in the PCG solver is suggested to avoid using a large block size that often increases the number of iterations needed to achieve convergence.

An improved parallel block Lanczos algorithm over GF(2) for integer factorization

2017 ◽  
Vol 379 ◽  
pp. 257-273 ◽  
Author(s):  
Laurence T. Yang ◽  
Ying Huang ◽  
Jun Feng ◽  
Qiwen Pan ◽  
Chunsheng Zhu
Keyword(s):  
Integer Factorization ◽  
Lanczos Algorithm ◽  
Block Lanczos
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