Results 121 to 130 of about 510,427 (158)
On Positive Semidefinite Modification Schemes for Incomplete Cholesky Factorization [PDF]
SIAM Journal of Scientific Computing, 2014 Incomplete Cholesky factorizations have long been important as preconditioners for use in solving large-scale symmetric positive-definite linear systems. In this paper, we focus on the relationship between two important positive semidefinite modification schemes that were introduced to avoid factorization breakdown, namely, the approach of Jennings and
Jennifer Scott, Miroslav Tūma
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On Signed Incomplete Cholesky Factorization Preconditioners for Saddle-Point Systems [PDF]
SIAM Journal of Scientific Computing, 2014 Limited-memory incomplete Cholesky factorizations can provide robust preconditioners for sparse symmetric positive-definite linear systems. In this paper, the focus is on extending the approach to sparse symmetric indefinite systems in saddle-point form.
Jennifer Scott, Miroslav Tūma
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Conditioning Analysis of Incomplete Cholesky Factorizations with Orthogonal Dropping [PDF]
SIAM Journal on Matrix Analysis and Applications, 2013 We analyze preconditioners based on incomplete Cholesky factorization in which each neglected (dropped) component is orthogonal to the approximation being kept. We present a general estimate for the condition number of the preconditioned system which only depends on the accuracy of individual approximations.
Artem Napov
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Improve Sparse Implicit Projection Via Incomplete Cholesky Factorization
2023 China Semiconductor Technology International Conference (CSTIC), 2023Xuan Zeng
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Incomplete Multilevel Cholesky Factorizations
SIAM Journal on Matrix Analysis and Applications, 2001Summary: Adaptive in-time local grid refinement techniques use multilevel local discretizations designed to achieve local accuracy. The changing nature of the matrix structure of the linear systems arising from the multilevel local discretizations requires flexible approximate factorizations that focus on local components and coordinate their ...
J. C. Díaz, K. Komara
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Incomplete Cholesky Factorizations with Limited Memory
SIAM Journal on Scientific Computing, 1999An incomplete Cholesky factorization is suggested for the solution of large-scale trust region subproblems and positive definite systems of linear equations. This factorization depends on a parameter \(p\) that specifies the amount of additional memory being available.
Chih-Jen Lin, Jorge J. Moré
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IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2023
Zhengqi Gao, Xuan Zeng, Yangfeng Su
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Zhengqi Gao, Xuan Zeng, Yangfeng Su
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Multisplitting Preconditioners Based on Incomplete Choleski Factorizations
SIAM Journal on Matrix Analysis and Applications, 1995Additive polynomial preconditioners for the conjugate gradient method, applied to a symmetric positive definite matrix, are presented. Their construction is based on multisplittings in incomplete Cholesky factorization. A sufficient condition is proved for the symmetry and positive definiteness of the preconditioner.
Bru R +3 more
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Algorithm 740: Fortran subroutines to compute improved incomplete Cholesky factorizations
ACM Transactions on Mathematical Software, 1995Efficient and reliable code to compute incomplete Cholesky factors of sparse matrices for use as preconditioners in a conjugate gradient algorithm is described. This code implements two recently developed, improved incomplete factorization algorithms. An efficient implementation of the standard incomplete Cholesky factorization is also included.
Mark T Jones, Paul E Plassmann
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MODIFLED INCOMPLETE CHOLESKY FACTORIZATION PRECONDITIONERS FOR A SYMMETRIC POSITIVE DEFINITE MATRIX
Bulletin of the Korean Mathematical Society, 2002 Variants of the modified incomplete Cholesky factorization for a symmetric positive definite matrix are proposed. This factorization is used for the preconditioned conjugate gradient algorithm. Spectral properties are discussed and numerical results are presented.
Yun, Jae Heon, Han, Yu Du
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