• LAPACK

  • Referenced in 1713 articles [sw00503]
  • possible performance, LAPACK requires that highly optimized block matrix operations be already implemented on each ... matrix multiplication and the solution of triangular systems with multiple right-hand sides. Because...
  • KLU

  • Referenced in 16 articles [sw06365]
  • relies on a permutation to Block Triangular Form (BTF), several methods for finding a fill ... looking LU factorization algorithm to factorize each block. The package is written...
  • Daesa

  • Referenced in 13 articles [sw14290]
  • tool. It also can construct a block-triangular form of the DAE, which ... exploited to solve it efficiently in a block-wise manner. This paper describes the theory...
  • PurityFiltration

  • Referenced in 10 articles [sw07656]
  • which is defined by a block-triangular matrix formed by equidimensional diagonal blocks. The linear...
  • SCASY

  • Referenced in 12 articles [sw03251]
  • ways of introducing blocking for solving matrix equations in reduced (quasi-triangular) form are reviewed ... successful approach is to combine recursion and blocking. We consider parallelization of algorithms for reduced ... solution to the reduced triangular systems. Parallelization of recursive blocked algorithms is done...
  • LIFT

  • Referenced in 3 articles [sw25813]
  • nested decomposition algorithm for solving lower block triangular linear programs. The lower block triangular structure...
  • recsy

  • Referenced in 8 articles [sw04139]
  • ways of introducing blocking for solving matrix equations in reduced (quasi-triangular) form are reviewed ... successful approach is to combine recursion and blocking. We consider parallelization of algorithms for reduced ... solution to the reduced triangular systems. Parallelization of recursive blocked algorithms is done...
  • SuiteSparseQR

  • Referenced in 45 articles [sw07348]
  • handled with Intel’s Threading Building Blocks library. The symbolic analysis and ordering phase ... where R11 is upper triangular with diagonal entries above a given tolerance. Next, the fill...
  • RRQR

  • Referenced in 22 articles [sw04673]
  • matrices. The main contribution is an efficient block algorithm for approximating an RRQR factorization, employing ... improved versions of the RRQR algorithms for triangular matrices orginally suggersted by Chandrasekaran and Ipsen...
  • MFEM

  • Referenced in 62 articles [sw09043]
  • finite element toolbox, that provides the building blocks for developing finite element algorithms ... classes for dealing with various types of triangular, quadrilateral, tetrahedral and hexahedral meshes and their...
  • ManiSolve

  • Referenced in 1 article [sw34623]
  • that its Jacobian is in bordered block lower triangular form with small diagonal blocks...
  • DGGHR3

  • Referenced in 7 articles [sw13050]
  • reduction of a matrix pair to Hessenberg-triangular (HT) form. In this paper, we discuss ... prototype implementation DGGHR3 of a general blocked algorithm...
  • DGGHRD

  • Referenced in 7 articles [sw13051]
  • reduction of a matrix pair to Hessenberg-triangular (HT) form. In this paper, we discuss ... prototype implementation DGGHR3 of a general blocked algorithm...
  • toms/782

  • Referenced in 22 articles [sw05211]
  • above)]. The main contribution is an efficient block algorithm for approximating an RRQR factorization, employing ... improved versions of the RRQR algorithms for triangular matrices originally suggested by {it S. Chandrasekaran...
  • Algorithm 865

  • Referenced in 2 articles [sw20200]
  • They exploit cache memory by using the block hybrid format proposed by the authors ... rearranging a matrix whose upper or lower-triangular part is packed by columns to this ... Cholesky factorization of the diagonal blocks since it is suitable for any positive-definite symmetric...
  • LIBRSB

  • Referenced in 0 articles [sw40544]
  • sparse matrix computations featuring the Recursive Sparse Blocks (RSB) matrix format. This format allows cache ... matrix-vector multiplication, triangular solution, rows/columns scaling, diagonal extraction / setting, blocks extraction, norm computation, formats...
  • randUTV

  • Referenced in 4 articles [sw30518]
  • randUTV: a blocked randomized algorithm for computing a rank-revealing UTV factorization. A randomized algorithm ... have orthonormal columns, and T is triangular (either upper or lower, whichever is preferred...
  • swSpTRSV

  • Referenced in 2 articles [sw30964]
  • level tile layout on Sunway architectures. Sparse triangular solve (SpTRSV) is one of the most ... core processor, which is the main building-block of the current world fastest supercomputer Sunway...
  • ANSYS

  • Referenced in 713 articles [sw00044]
  • ANSYS offers a comprehensive software suite that spans...