
Algorithm 740
 Referenced in 4 articles
[sw04691]
 Fortran subroutines to compute improved incomplete Cholesky factorizations An efficient and reliable code to compute ... incomplete Cholesky factors of sparse matrices for use as preconditioners in a conjugate gradient algorithm ... efficient implementation of the standard incomplete Cholesky factorization is also included...

symamd
 Referenced in 6 articles
[sw08565]
 tends to have a sparser Cholesky factor than S. To find the ordering...

QPBOX
 Referenced in 6 articles
[sw04799]
 iteration, and up and downdating of Cholesky factorization. Results of extensive testing and comparison with...

Algorithm 865
 Referenced in 2 articles
[sw20200]
 Algorithm 865: Fortran 95 subroutines for Cholesky factorization in block hybrid format. We present subroutines ... Cholesky factorization of a positivedefinite symmetric matrix and for solving corresponding sets of linear ... subroutine that is used for the Cholesky factorization of the diagonal blocks since...

Algorithm 977
 Referenced in 2 articles
[sw25562]
 matrix computations, the combination of the QR factorization and an SVD computation routine ... Further, when combined with pivoted Cholesky factorization, xGESVDQ provides numerically accurate and fast solvers (designated ... problem. For instance, using accurately computed Cholesky factor, xPSEVC computes all eigenvalues...

Pfaffian
 Referenced in 4 articles
[sw10808]
 kind of LU (similar to Cholesky’s factorization) decomposition (under congruence) of arbitrary skewsymmetric...

KKTDirect
 Referenced in 1 article
[sw04032]
 factorization, giving rise to a ”signed Cholesky” factorization. A modified minimumdegreelike algorithm which ... possible. For example, a highly efficient Cholesky factorization routine, based on separate symbolic and numerical...

DPOTF3
 Referenced in 1 article
[sw10056]
 Level3 Cholesky factorization routines improve performance of many Cholesky algorithms. Four routines called DPOTF3i ... Blocked Packed Format) Cholesky factorization and LAPACK routine DPOTRF. Performance of routines DPOTF3i are still...

PoLAPACK
 Referenced in 1 article
[sw01596]
 with algorithmic blocking LU, QR, and Cholesky factorizations are the most widely used methods ... vector and parallel computers. Most of these factorization routines are implemented with blockpartitioned algorithms ... present parallel LU, QR, and Cholesky factorization routines with an `algorithmic blocking’ on twodimensional...

CholQR
 Referenced in 3 articles
[sw13049]
 Mixedprecision Cholesky QR factorization and its case studies on multicore CPU with multiple gpus ... columns of a dense matrix, the Cholesky QR (CholQR) requires only one global reduction between...

symPACK
 Referenced in 1 article
[sw16317]
 Asynchronous Taskbased FanBoth Sparse Cholesky Solver. Systems of linear equations arise ... zero. Direct methods based on matrix factorizations are sometimes needed to ensure accurate solutions ... storage cost required for factorization. When the factorization is performed on largescale distributed memory ... dynamic scheduling in implementing sparse Cholesky factorization (symPACK) on largescale distributed memory platforms...

HSL_MI30
 Referenced in 1 article
[sw28020]
 indeﬁnite saddlepoint system: signed incomplete Cholesky factorization...

jmcm
 Referenced in 1 article
[sw23057]
 decomposition (ACD) and hyperspherical parameterization of Cholesky factor (HPC). We then introduce our newly developed...

IPPCG
 Referenced in 3 articles
[sw04830]
 preconditioner is factorized in a Cholesky like form by means of the BLKFCLT routine...

FACTORIZE
 Referenced in 2 articles
[sw10039]
 selection of the best factorization method (LU, Cholesky, LDL T , QR, or a complete orthogonal ... does the right thing by factorizing A and solving the corresponding triangular systems...

DRIC
 Referenced in 22 articles
[sw12610]
 given with the dynamic modified incomplete factorization methods of O. Axelsson and V. A. Barker ... with the relaxed incomplete Cholesky (RIC) method of O. Axelsson and G. Lindskog [Numer. Math...

Cholesky solver
 Referenced in 1 article
[sw08744]
 Cholesky outofcore factorization. Frequently, the computational core in general engineering simulation software ... direct sparse linear solvers such as Cholesky, LDL T , or LU are perfect black boxes ... core implementation for the Cholesky solver in order to overcome the memory problem ... problem matrix A and the factor L whose complete data are stored in temporary disk...

CholeskyQR2
 Referenced in 3 articles
[sw14461]
 algorithm for computing a tallskinny QR factorization, and TSQR is known to be much ... classical Householder QR algorithm. The Cholesky QR algorithm is another very simple and fast communication ... that an algorithm that simply repeats Cholesky QR twice, which we call CholeskyQR2, gives excellent ... whereas that of TSQR is a QR factorization, whose highperformance implementation is more difficult...

IEL
 Referenced in 1 article
[sw13814]
 equations, which is factorized by an outofcore parallel Cholesky decomposition solver. The coupling...