
LINPACK
 Referenced in 394 articles
[sw04209]
 square. In addition, the package computes the QR and singular value decompositions of rectangular matrices ... leastsquares problems. LINPACK uses columnoriented algorithms to increase efficiency by preserving locality...

ARPACK
 Referenced in 581 articles
[sw04218]
 operations. This software is based upon an algorithmic variant of the Arnoldi process called ... Arnoldi/Lanczos process with the Implicitly Shifted QR technique that is suitable for large scale problems...

LAPACK
 Referenced in 1178 articles
[sw00503]
 problems. The associated matrix factorizations (LU, Cholesky, QR, SVD, Schur, generalized Schur) are also provided ... LAPACK addresses this problem by reorganizing the algorithms to use block matrix operations, such...

Chebfun
 Referenced in 155 articles
[sw05897]
 Chebfun is a collection of algorithms and a software system in objectoriented MATLAB that ... analogues of linear algebra notions like the QR decomposition and the SVD, and solves ordinary...

Algorithm 800
 Referenced in 7 articles
[sw04405]
 Algorithm 800. Fortran 77 subroutines for computing the eigenvalues of Hamiltonian matrices. I: The square ... needed by the general QR algorithm. Routines are provided for computing the squarereduced form ... execution times compared to the general QR routine, DGEEVX, from the LAPACK library. The authors...

RRQR
 Referenced in 19 articles
[sw04673]
 Algorithm 782: Codes for rankrevealing QR factorizations of dense matrices. This article describes ... QR (RRQR) factorizations of dense matrices. The main contribution is an efficient block algorithm...

Algorithm 730
 Referenced in 5 articles
[sw14348]
 reliable and competitive with the general QR algorithm applied to this problem. Moreover, the algorithm...

Algorithm 953
 Referenced in 2 articles
[sw17440]
 parallel library software for the multishift QR algorithm with aggressive early deflation. Library software implementing ... parallel smallbulge multishift QR algorithm with Aggressive Early Deflation (AED) targeting distributed memory high ... recent developments of the parallel multishift QR algorithm [the firs author et al., SIAM ... been removed in the parallel multishift QR algorithm. A performance model is established to explain...

toms/782
 Referenced in 17 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 ... main contribution is an efficient block algorithm for approximating an RRQR factorization, employing a windowed...

CholeskyQR2
 Referenced in 2 articles
[sw14461]
 simple and communicationavoiding algorithm for computing a tallskinny QR factorization on a large ... communicationavoiding algorithm for computing a tallskinny QR factorization, and TSQR is known ... stable as the classical Householder QR algorithm. The Cholesky QR algorithm is another very simple ... points out that an algorithm that simply repeats Cholesky QR twice, which we call CholeskyQR2...

TOMS686
 Referenced in 7 articles
[sw04785]
 Algorithm 686: FORTRAN subroutines for updating the QR decomposition...

AggDef2
 Referenced in 3 articles
[sw10244]
 LAPACK subroutine and is the preferred algorithm for this purpose. In this paper, we incorporate ... been applied successfully to the Hessenberg QR algorithm. Extensive numerical experiments show that aggressive early...

Algorithm 826
 Referenced in 3 articles
[sw04468]
 Algorithm 826: A parallel eigenvalue routine for complex Hessenberg matrices A code for computing ... directly computed using a parallel $QR$ algorithm.This parallel complex Schur decomposition routine was developed ... implement a complex multiple bulge $QR$ algorithm. This also required the development of new auxiliary...

SuiteSparseQR
 Referenced in 15 articles
[sw07348]
 Algorithm 915, SuiteSparseQR: Multifrontal multithreaded rankrevealing sparse QR factorization SuiteSparseQR is a sparse...

Algorithm 844
 Referenced in 15 articles
[sw04407]
 Algorithm 844: Computing sparse reducedrank approximations to sparse matrices In many applications  latent semantic ... traditional decompositions, like the singular value and QR decompositions, are not in general sparse ... variant of the classical GramSchmidt algorithm, called the quasiGramSchmidtalgorithm, to obtain ... SPQR, approximation, is a pivoted, $Q$less QR approximation of the form $(XR11...

DAMRO1
 Referenced in 2 articles
[sw07446]
 rotor speed are obtained using the QR algorithm using the DAMRO1 program and compared...

Algorithm 854
 Referenced in 15 articles
[sw07345]
 algorithms are supplemented with balancing and block algorithms which can lead to considerable accuracy ... product, an efficient implementation for computing symplectic QR decompositions is provided. We demonstrate the usefulness...

QPSchur
 Referenced in 13 articles
[sw06918]
 every working set considered by the algorithm. Therefore, this method is not appropriate ... numerically stable as approaches using a QR factorization. However, we show that ... numerical stability of this Schur complement algorithm. The use of the objectoriented QP solver...

PoLAPACK
 Referenced in 1 article
[sw01596]
 PoLAPACK: Parallel factorization routines with algorithmic blocking LU, QR, and Cholesky factorizations are the most ... factorization routines are implemented with blockpartitioned algorithms in order to perform matrixmatrix operations ... generate the maximum performance of an algorithm. Therefore, the data matrix should be distributed with ... present parallel LU, QR, and Cholesky factorization routines with an `algorithmic blocking’ on twodimensional...

Blendenpik
 Referenced in 16 articles
[sw09210]
 implementations of existing stateoftheart algorithms, and it is numerically backward stable. More ... achieves residuals similar to those of direct QR factorizationbased solvers (LAPACK), outperforms LAPACK...