scholarly journals INCOMPLETE CHOLESKY FACTORIZATION IN FIXED MEMORY WITH FLEXIBLE DROP-TOLERANCE STRATEGY

2014 ◽  
pp. 22-29
Author(s):  
Sergey Saukh
Keyword(s):  
Large Scale ◽  
Trust Region ◽  
Positive Definite ◽  
Cholesky Factorization ◽  
Systems Of Equations ◽  
Factor Matrix ◽  
Irregular Distribution ◽  
Tolerance Strategy ◽  
Incomplete Cholesky Factorization ◽  
Two Parameter

We propose an incomplete Cholesky factorization for the solution of large positive definite systems of equations and for the solution of large-scale trust region sub-problems. The factorization is based on the two- parameter (m, p) drop-tolerance strategy for insignificant elements in the incomplete factor matrix. The factorization proposed essentially reduces the negative processes of irregular distribution and accumulation of errors in factor matrix and provides the optimal rate of memory filling with essential nonzero elements. On the contrary to the known p - retain and t - drop-tolerance strategies, the (m, p) strategy allows to form the factor matrix in fixed memory.

scholarly journals Fast kernel k-means clustering using incomplete Cholesky factorization

2021 ◽  
Vol 402 ◽  
pp. 126037
Author(s):  
Li Chen ◽  
Shuisheng Zhou ◽  
Jiajun Ma ◽  
Mingliang Xu
Keyword(s):  
Cholesky Factorization ◽  
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].

PSVM: Parallel Support Vector Machines with Incomplete Cholesky Factorization

2012 ◽  
pp. 109-126
Author(s):  
Edward Y. Chang ◽  
Hongjie Bai ◽  
Kaihua Zhu ◽  
Hao Wang ◽  
Jian Li ◽  
...  
Keyword(s):  
Support Vector Machines ◽  
Cholesky Factorization ◽  
Support Vector ◽  
Vector Machines ◽  
Incomplete Cholesky Factorization
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