• # LINPACK

• Referenced in 394 articles [sw04209]
• square. In addition, the package computes the QR and singular value decompositions of rectangular matrices ... least-squares problems. LINPACK uses column-oriented 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 object-oriented 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 square-reduced 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 rank-revealing QR factorizations of dense matrices. This article describes ... QR (RRQR) factorizations of dense matrices. The main contribution is an efficient block algorithm...
• # Algorithm 953

• Referenced in 2 articles [sw17440]
• parallel library software for the multishift QR algorithm with aggressive early deflation. Library software implementing ... parallel small-bulge 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 rank-revealing QR factorizations of dense matrices This article describes ... timing drivers for computing rank-revealing 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 communication-avoiding algorithm for computing a tall-skinny QR factorization on a large ... communication-avoiding algorithm for computing a tall-skinny 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...
• # 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...
• # Algorithm 844

• Referenced in 15 articles [sw04407]
• Algorithm 844: Computing sparse reduced-rank 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 Gram-Schmidt algorithm, called the quasi-Gram-Schmidt-algorithm, to obtain ... SPQR, approximation, is a pivoted, $Q$-less QR approximation of the form \$(XR11...
• # 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 object-oriented 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 block-partitioned algorithms in order to perform matrix-matrix 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 two-dimensional...
• # Blendenpik

• Referenced in 16 articles [sw09210]
• implementations of existing state-of-the-art algorithms, and it is numerically backward stable. More ... achieves residuals similar to those of direct QR factorization-based solvers (LAPACK), outperforms LAPACK...