scholarly journals Indefinite Ruhe’s Variant of the Block Lanczos Method for Solving the Systems of Linear Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
M. Ghasemi Kamalvand ◽  
K. Niazi Asil
Keyword(s):  
Scalar Product ◽  
Hermitian Matrix ◽  
Linear Equations ◽  
Lanczos Method ◽  
Krylov Methods ◽  
Block Arnoldi ◽  
Systems Of Linear Equations ◽  
Block Lanczos ◽  
Lanczos Methods ◽  
Block Lanczos Method

In this paper, we equip Cn with an indefinite scalar product with a specific Hermitian matrix, and our aim is to develop some block Krylov methods to indefinite mode. In fact, by considering the block Arnoldi, block FOM, and block Lanczos methods, we design the indefinite structures of these block Krylov methods; along with some obtained results, we offer the application of this methods in solving linear systems, and as the testifiers, we design numerical examples.

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.

Convergence of the block Lanczos method for eigenvalue clusters

2014 ◽  
Vol 131 (1) ◽  
pp. 83-113 ◽  
Author(s):  
Ren-Cang Li ◽  
Lei-Hong Zhang
Keyword(s):  
Lanczos Method ◽  
Block Lanczos ◽  
Block Lanczos Method

Modal Analysis of Crankshaft for Two-Stroke Marine Diesel Engine Based on Block Lanczos Method

2014 ◽  
Vol 998-999 ◽  
pp. 434-437
Author(s):  
Gong Zhi Yu ◽  
Hong Liang Yu ◽  
Da Wei Wang
Keyword(s):  
Diesel Engine ◽  
Modal Analysis ◽  
Natural Frequencies ◽  
Lanczos Method ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Marine Diesel Engine ◽  
Marine Diesel ◽  
Block Lanczos ◽  
Block Lanczos Method

Modal analysis of crankshaft for two-stroke marine diesel engine is carried out on the block lanczos method. The finite element models of crankshaft is created in ANSYS. The crankshaft first 13 natural frequencies and mode shapes are shown as the result and lay the foundation for optimal design of the crankshaft and dynamic response.

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