• LAPACK

  • Referenced in 1222 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 598 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...
  • ALCON

  • Referenced in 33 articles [sw05315]
  • Newton method is used where the QR-factorization of the Jacobian is computed only once...
  • SPARSE-QR

  • 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...
  • SuiteSparseQR

  • Referenced in 17 articles [sw07348]
  • SuiteSparseQR: Multifrontal multithreaded rank-revealing 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...
  • RRQR

  • Referenced in 20 articles [sw04673]
  • 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. The main contribution...
  • toms/782

  • Referenced in 18 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...
  • COLAMD

  • Referenced in 19 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...
  • QPSchur

  • Referenced in 14 articles [sw06918]
  • numerically stable as approaches using a QR factorization. However, we show that...
  • ScaLAPACK

  • Referenced in 331 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...
  • Blendenpik

  • Referenced in 17 articles [sw09210]
  • residuals similar to those of direct QR factorization-based solvers (LAPACK), outperforms LAPACK by large ... factors, and scales significantly better than any QR-based solver...
  • MIQR

  • Referenced in 5 articles [sw07242]
  • This paper describes a multilevel incomplete QR factorization for solving large sparse least-squares 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 2 articles [sw14461]
  • algorithm for computing a tall-skinny QR factorization on a large-scale parallel system. Designing ... algorithm for computing a tall-skinny 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 high-performance implementation is more difficult...
  • QRUP

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

  • Referenced in 1 article [sw10036]
  • SuiteSparseQR: multifrontal multithreaded rank-revealing sparse QR factorization”, ACM Trans. Math. Softw ... high-performance routine for forming QR factorizations of large, sparse matrices. It returns an estimate...
  • VXQR1

  • Referenced in 1 article [sw05273]
  • Derivative-free unconstrained optimization based on QR factorizations (Matlab...
  • QRUP_

  • Referenced in 1 article [sw07228]
  • FORTRAN Routines for Updating QR Factorizations...
  • CholQR

  • Referenced in 1 article [sw13049]
  • Mixed-precision 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...
  • PoLAPACK

  • Referenced in 1 article [sw01596]
  • routines 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 block-partitioned algorithms ... matrix. We present parallel LU, QR, and Cholesky factorization routines with an `algorithmic blocking...
  • CULA

  • Referenced in 5 articles [sw12745]
  • results from factorizations such as LU decomposition, singular value decomposition and QR decomposition along with...