An Algorithm for Chaotic Masking and Its Blind Extraction of Image Information in Positive Definite System

2018 ◽  
pp. 428-436
Author(s):  
Xinwu Chen ◽  
Yaqin Xie ◽  
Erfu Wang ◽  
Danyang Qin
Keyword(s):  
Positive Definite ◽  
Image Information ◽  
Blind Extraction ◽  
Positive Definite System

scholarly journals A parallel Cholesky algorithm for the solution of symmetric linear systems

2004 ◽  
Vol 2004 (25) ◽  
pp. 1315-1327
Author(s):  
R. R. Khazal ◽  
M. M. Chawla
Keyword(s):  
Parallel Algorithm ◽  
Linear Systems ◽  
Triangular Matrix ◽  
Coefficient Matrix ◽  
Positive Definite ◽  
Identity Matrix ◽  
Lower Triangular Matrix ◽  
Elimination Method ◽  
Lower Triangular ◽  
Positive Definite System

For the solution of symmetric linear systems, the classical Cholesky method has proved to be difficult to parallelize. In the present paper, we first describe an elimination variant of Cholesky method to produce a lower triangular matrix which reduces the coefficient matrix of the system to an identity matrix. Then, this elimination method is combined with the partitioning method to obtain a parallel Cholesky algorithm. The total serial arithmetical operations count for the parallel algorithm is of the same order as that for the serial Cholesky method. The present parallel algorithm could thus perform withefficiencyclose to 1 if implemented on a multiprocessor machine. We also discuss theexistenceof the parallel algorithm; it is shown that for a symmetric and positive definite system, the presented parallel Cholesky algorithm is well defined and will run to completion.

An Approximate Minimal Elimination Ordering Scheme

2011 ◽  
Vol 268-270 ◽  
pp. 1533-1536
Author(s):  
Lu Yao ◽  
Zheng Hua Wang ◽  
Wei Cao ◽  
Zong Zhe Li ◽  
Yong Xian Wang
Keyword(s):  
Factorization Method ◽  
Positive Definite ◽  
Cholesky Factorization ◽  
Running Time ◽  
Symmetric Positive Definite ◽  
Matrix Ordering ◽  
Positive Definite System

Matrix ordering is a key technique when applying Cholesky factorization method to solving sparse symmetric positive definite system Ax = b. In view of some known minimal elimination ordering methods, an efficient heuristic approximate minimal elimination ordering scheme is proposed, which has the total running time of O(n+m). It is noteworthy that the algorithm can not only find a good ordering efficiently, but also achieve the result of symbolic factorization simultaneously.

Sign in / Sign up

Export Citation Format

Share Document