
LAPACK
 Referenced in 1677 articles
[sw00503]
 value problems. The associated matrix factorizations (LU, Cholesky, QR, SVD, Schur, generalized Schur) are also ... computations such as reordering of the Schur factorizations and estimating condition numbers. Dense and banded...

ARPACK
 Referenced in 822 articles
[sw04218]
 Arnoldi/Lanczos process with the Implicitly Shifted QR technique that is suitable for large scale problems ... many standard problems, a matrix factorization is not required. Only the action of the matrix...

SuiteSparseQR
 Referenced in 33 articles
[sw07348]
 SuiteSparseQR: Multifrontal multithreaded rankrevealing sparse QR factorization SuiteSparseQR is a sparse QR factorization package ... sufficiently large problems, the resulting sparse QR factorization obtains a substantial fraction of the theoretical...

ALCON
 Referenced in 36 articles
[sw05315]
 Newton method is used where the QRfactorization of the Jacobian is computed only once...

COLAMD
 Referenced in 30 articles
[sw00145]
 rows and columns of the matrix being factorized. These orderings are computed by COLAMD ... COLAMD is also suitable for sparse QR factorization, and the factorization of matrices...

SPARSEQR
 Referenced in 17 articles
[sw05215]
 Sparse QR factorization in MATLAB In the recently presented sparse matrix extension of MATLAB, there ... routine for sparse QR factorization. Sparse linear least squares problems are instead solved ... describe a multifrontal method for sparse QR factorization and its implementation in MATLAB ... accurate as the methods based on QR factorization...

Blendenpik
 Referenced in 41 articles
[sw09210]
 residuals similar to those of direct QR factorizationbased solvers (LAPACK), outperforms LAPACK by large ... factors, and scales significantly better than any QRbased solver...

RRQR
 Referenced in 22 articles
[sw04673]
 Algorithm 782: Codes for rankrevealing QR factorizations of dense matrices. This article describes ... timing drivers for computing rankrevealing QR (RRQR) factorizations of dense matrices. The main contribution...

toms/782
 Referenced in 22 articles
[sw05211]
 Algorithm 782: Codes for rankrevealing QR factorizations of dense matrices. This article describes ... timing drivers for computing rankrevealing QR (RRQR) factorizations of dense matrices [cf. the authors...

ScaLAPACK
 Referenced in 413 articles
[sw00830]
 least squares problems, orthogonal and generalized orthogonal factorizations, orthogonal transformation routines, reductions to upper Hessenberg ... core solvers for LU, Cholesky, and QR, the matrix sign function for eigenproblems...

QPSchur
 Referenced in 16 articles
[sw06918]
 numerically stable as approaches using a QR factorization. However, we show that...

SingularIntegralEquations
 Referenced in 10 articles
[sw22771]
 operations using an adaptive QR factorization, where m is the bandwidth ... operations by precaching the QR factorization when the same operator is used for multiple...

MIQR
 Referenced in 9 articles
[sw07242]
 This paper describes a multilevel incomplete QR factorization for solving large sparse leastsquares problems ... algorithm builds the factorization by exploiting structural orthogonality in general sparse matrices. At any given ... with a standard QR or incomplete QR factorization. Dropping strategies are employed throughout the levels ... with the standard incomplete QR preconditioner, the robust incomplete factorization preconditioner, and the algebraic recursive...

CholeskyQR2
 Referenced in 8 articles
[sw14461]
 algorithm for computing a tallskinny QR factorization on a largescale parallel system. Designing ... algorithm for computing a tallskinny QR factorization, and TSQR is known to be much ... stable as the classical Householder QR algorithm. The Cholesky QR algorithm is another very simple ... whereas that of TSQR is a QR factorization, whose highperformance implementation is more difficult...

CholQR
 Referenced in 11 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...

Algorithm 977
 Referenced in 3 articles
[sw25562]
 novelty is an extra step, the QR factorization with column (or complete row and column ... matrix computations, the combination of the QR factorization and an SVD computation routine...

Algorithm 980
 Referenced in 2 articles
[sw22549]
 Algorithm 980: Sparse QR Factorization on the GPU. Sparse matrix factorization involves ... GPUs). We present a sparse multifrontal QR factorization method that meets this challenge ... method on a multicore CPU. Our method factorizes many frontal matrices in parallel and keeps ... scheduler algorithm extends the communicationavoiding QR factorization for dense matrices by exploiting more parallelism...

QRUP
 Referenced in 3 articles
[sw04458]
 triangular factor of a sparse QR factorization when columns are added and deleted...

SPQR_RANK
 Referenced in 2 articles
[sw10036]
 SuiteSparseQR: multifrontal multithreaded rankrevealing sparse QR factorization”, ACM Trans. Math. Softw ... highperformance routine for forming QR factorizations of large, sparse matrices. It returns an estimate...

VXQR1
 Referenced in 2 articles
[sw05273]
 Derivativefree unconstrained optimization based on QR factorizations (Matlab...