scholarly journals MODIFLED INCOMPLETE CHOLESKY FACTORIZATION PRECONDITIONERS FOR A SYMMETRIC POSITIVE DEFINITE MATRIX

2002 ◽  
Vol 39 (3) ◽  
pp. 495-509 ◽  
Author(s):  
Jae-Heon Yun ◽  
Yu-Du Han
Keyword(s):  
Positive Definite Matrix ◽  
Positive Definite ◽  
Cholesky Factorization ◽  
Symmetric Positive Definite Matrix ◽  
Symmetric Positive Definite ◽  
Incomplete Cholesky Factorization

A CONSTRAINT PRECONDITIONER FOR SOLVING SYMMETRIC POSITIVE DEFINITE SYSTEMS AND APPLICATION TO THE HELMHOLTZ EQUATIONS AND POISSON EQUATIONS

2010 ◽  
Vol 15 (3) ◽  
pp. 299-311 ◽  
Author(s):  
Zhuo-Hong Huang ◽  
Ting-Zhu Huang
Keyword(s):  
Numerical Experiments ◽  
Positive Definite ◽  
Cholesky Factorization ◽  
Helmholtz Equations ◽  
Poisson Equations ◽  
Symmetric Positive Definite ◽  
Incomplete Cholesky Factorization ◽  
Preconditioned Matrix ◽  
Factorization Methods ◽  
Number Of Iterations

In this paper, first, by using the diagonally compensated reduction and incomplete Cholesky factorization methods, we construct a constraint preconditioner for solving symmetric positive definite linear systems and then we apply the preconditioner to solve the Helmholtz equations and Poisson equations. Second, according to theoretical analysis, we prove that the preconditioned iteration method is convergent. Third, in numerical experiments, we plot the distribution of the spectrum of the preconditioned matrix M−1A and give the solution time and number of iterations comparing to the results of [5, 19].

scholarly journals A randomized algorithm for approximating the log determinant of a symmetric positive definite matrix

2017 ◽  
Vol 533 ◽  
pp. 95-117 ◽  
Author(s):  
Christos Boutsidis ◽  
Petros Drineas ◽  
Prabhanjan Kambadur ◽  
Eugenia-Maria Kontopoulou ◽  
Anastasios Zouzias
Keyword(s):  
Randomized Algorithm ◽  
Positive Definite Matrix ◽  
Positive Definite ◽  
Symmetric Positive Definite Matrix ◽  
Symmetric Positive Definite
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