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

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

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

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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