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

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.

Projective Block Lanczos Algorithm for Dense, Hermitian Eigensystems

1996 ◽  
Vol 124 (1) ◽  
pp. 146-161 ◽  
Author(s):  
Frank Webster ◽  
Gen-Ching Lo
Keyword(s):  
Lanczos Algorithm ◽  
Block Lanczos
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