A fast LDL-factorization approach for large sparse positive definite system and its application to one-to-one marketing optimization computation

2007 ◽  
Vol 4 (1) ◽  
pp. 88-94 ◽  
Author(s):  
Min Wu ◽  
Bei He ◽  
Jin-Hua She
Keyword(s):  
Positive Definite ◽  
Factorization Approach ◽  
One To One ◽  
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.

A Support Program

1994 ◽  
Vol 25 (2) ◽  
pp. 112-114 ◽  
Author(s):  
Henna Grunblatt ◽  
Lisa Daar
Keyword(s):  
Hearing Aids ◽  
School Counselor ◽  
Support Program ◽  
Educational Audiology ◽  
Part Program ◽  
One To One

A program for providing information to children who are deaf about their deafness and addressing common concerns about deafness is detailed. Developed by a school audiologist and the school counselor, this two-part program is geared for children from 3 years to 15 years of age. The first part is an educational audiology program consisting of varied informational classes conducted by the audiologist. Five topics are addressed in this part of the program, including basic audiology, hearing aids, FM systems, audiograms, and student concerns. The second part of the program consists of individualized counseling. This involves both one-to-one counseling sessions between a student and the school counselor, as well as conjoint sessions conducted—with the student’s permission—by both the audiologist and the school counselor.

Review of One to One: The Experience of Psychotherapy.

1989 ◽  
Vol 34 (10) ◽  
pp. 958-958
Author(s):  
No authorship indicated
Keyword(s):  
One To One
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