Redundancy techniques and fast algorithms for a special large linear system

Computing ◽  
1977 ◽  
Vol 18 (4) ◽  
pp. 317-327 ◽  
Author(s):  
D. K. Lam ◽  
A. Wouk
Keyword(s):  
Linear System ◽  
Fast Algorithms ◽  
Large Linear System

Analysis of the binary complexity of asymptotically fast algorithms for linear system solving

1988 ◽  
Vol 22 (2) ◽  
pp. 41-49 ◽  
Author(s):  
Brent Gregory ◽  
Erich Kaltofen
Keyword(s):  
Linear System ◽  
Fast Algorithms

scholarly journals Fast verification for the Perron pair of an irreducible nonnegative matrix

2021 ◽  
Vol 37 ◽  
pp. 402-415
Author(s):  
Shinya Miyajima
Keyword(s):  
Linear System ◽  
Error Bounds ◽  
Computational Efficiency ◽  
Nonnegative Matrix ◽  
Fast Algorithms ◽  
Coefficient Matrix ◽  
Numerical Results ◽  
Perron Root ◽  
Irreducible Nonnegative Matrix

Fast algorithms are proposed for calculating error bounds for a numerically computed Perron root and vector of an irreducible nonnegative matrix. Emphasis is put on the computational efficiency of these algorithms. Error bounds for the root and vector are based on the Collatz--Wielandt theorem, and estimating a solution of a linear system whose coefficient matrix is an $M$-matrix, respectively. We introduce a technique for obtaining better error bounds. Numerical results show properties of the algorithms.

Fast algorithms for finding the solution of CUPL-Toeplitz linear system from Markov chain

2021 ◽  
Vol 396 ◽  
pp. 125859
Author(s):  
Yaru Fu ◽  
Xiaoyu Jiang ◽  
Zhaolin Jiang ◽  
Seongtae Jhang
Keyword(s):  
Markov Chain ◽  
Linear System ◽  
Fast Algorithms

Control of a large linear system through system subdivision

1977 ◽  
Vol 124 (8) ◽  
pp. 725
Author(s):  
P. Linga Reddy ◽  
B.S. Rao
Keyword(s):  
Linear System ◽  
Large Linear System

scholarly journals Locally-synchronous, iterative solver for Fourier-based homogenization

2021 ◽  
Author(s):  
R. Glüge ◽  
H. Altenbach ◽  
S. Eisenträger
Keyword(s):  
Linear System ◽  
Complete Solution ◽  
Iterative Solvers ◽  
Iterative Solver ◽  
System Matrix ◽  
Solution Vector ◽  
Homogenization Problem ◽  
Homogenization Approach ◽  
Large Linear System ◽  
Constitutive Tensor

AbstractWe use the algebraic orthogonality of rotation-free and divergence-free fields in the Fourier space to derive the solution of a class of linear homogenization problems as the solution of a large linear system. The effective constitutive tensor constitutes only a small part of the solution vector. Therefore, we propose to use a synchronous and local iterative method that is capable to efficiently compute only a single component of the solution vector. If the convergence of the iterative solver is ensured, i.e., the system matrix is positive definite and diagonally dominant, it outperforms standard direct and iterative solvers that compute the complete solution. It has been found that for larger phase contrasts in the homogenization problem, the convergence is lost, and one needs to resort to other linear system solvers. Therefore, we discuss the linear system’s properties and the advantages as well as drawbacks of the presented homogenization approach.

Chaos in a manifold piecewise linear system

1981 ◽  
Vol 64 (10) ◽  
pp. 9-17 ◽  
Author(s):  
Toshimichi Saito ◽  
Hiroichi Fujita
Keyword(s):  
Linear System ◽  
Piecewise Linear ◽  
Piecewise Linear System

Linear system reduction using approximate moment matching

1990 ◽  
Vol 137 (5) ◽  
pp. 322
Author(s):  
M. Bettayeb ◽  
U.M. Al-Saggaf
Keyword(s):  
Linear System ◽  
Moment Matching ◽  
System Reduction

Impossibility of steady squeezing for two-mode linear system without self-action

1991 ◽  
Vol 1 (9) ◽  
pp. 1217-1227 ◽  
Author(s):  
A. A. Bakasov ◽  
N. V. Bakasova ◽  
E. K. Bashkirov ◽  
V. Chmielowski
Keyword(s):  
Linear System
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