• # LAPACK

• Referenced in 1702 articles [sw00503]
• systems of equations, eigenvalue problems, and singular value problems. The associated matrix factorizations (LU, Cholesky ... algorithms to use block matrix operations, such as matrix multiplication, in the innermost loops. These ... performance, LAPACK requires that highly optimized block matrix operations be already implemented on each machine ... various types of matrix multiplication and the solution of triangular systems with multiple right-hand...
• # SuperLU

• Referenced in 195 articles [sw00930]
• large, sparse, nonsymmetric systems of linear equations on high performance machines. The library is written ... decomposition with partial pivoting and triangular system solves through forward and back substitution ... triangular solves are performed only for square matrices. The matrix columns may be preordered (before...
• # SCASY

• Referenced in 12 articles [sw03251]
• introducing blocking for solving matrix equations in reduced (quasi-triangular) form are reviewed. Most common ... that the computations are performed on submatrices (matrix blocks). Another successful approach is to combine ... consider parallelization of algorithms for reduced matrix equations at two levels: globally in a distributed ... compute the solution to the reduced triangular systems. Parallelization of recursive blocked algorithms is done...
• # SuperLU-DIST

• Referenced in 90 articles [sw00002]
• large, sparse, nonsymmetric systems of linear equations on high performance machines. The library is written ... decomposition with partial pivoting and triangular system solves through forward and back substitution ... triangular solves are performed only for square matrices. The matrix columns may be preordered (before...
• # recsy

• Referenced in 7 articles [sw04139]
• introducing blocking for solving matrix equations in reduced (quasi-triangular) form are reviewed. Most common ... that the computations are performed on submatrices (matrix blocks). Another successful approach is to combine ... consider parallelization of algorithms for reduced matrix equations at two levels: globally in a distributed ... compute the solution to the reduced triangular systems. Parallelization of recursive blocked algorithms is done...
• # TAUCS

• Referenced in 32 articles [sw04014]
• Matrix Operations. Matrix-vector multiplication, triangular solvers, matrix reordering. Matrix Input/Output. Routines to read ... read matrices in Harwell-Boeing format. Matrix Generators. Routines that generate finite-differences discretizations ... dimensional partial differential equations. Useful for testing the solvers. Iterative Solvers. Preconditioned conjugate-gradients...
• # OAHM

• Referenced in 3 articles [sw01076]
• equations in which the matrix A of coefficients is an M-matrix such that each ... element in the upper/lower triangular part is greater than or equal to the respective element...
• # PurityFiltration

• Referenced in 10 articles [sw07656]
• which is defined by a block-triangular matrix formed by equidimensional diagonal blocks. The linear ... underdetermined/overdetermined linear systems of partial differential equations can be explicitly integrated by the Maple package...
• # CIMGS

• Referenced in 12 articles [sw17583]
• complete Cholesky factorization of the normal equations. Theoretical results show that the CIMGS factorization ... numerically, even when the matrix is not an M-matrix. When the drop set satisfies ... easily verified (or enforced) property, the upper triangular factor CIMGS generates is the same...
• # TUBA3

• Referenced in 8 articles [sw06145]
• method for creating a class of triangular $C^{1}$ finite elements Finite elements providing ... problems where the underlying partial differential equation is of fourth order, such as beam ... TUBA family of plate elements for the matrix displacement method”, Aeronautical Journal of the Royal...
• # WSSMP

• Referenced in 4 articles [sw33235]
• sparse linear solver. The Watson Symmetric Sparse Matrix Package, WSSMP, is a high-performance, robust ... solving large sparse symmetric systems of linear equations. It can can be used ... multifrontal algorithms for sparse symmetric factorization and triangular solves. Sparse symmetric factorization in WSSMP...
• # Algorithm 982

• Referenced in 2 articles [sw22551]
• homogeneous triangular systems of first-order linear initial-value ordinary differential equations with constant coefficients ... matrix using a simple recurrence. Computing the solutions of the system from that matrix ... matrix. It is not necessary to compute the exponential of a general triangular matrix. Although...
• # Algorithm 865

• Referenced in 2 articles [sw20200]
• solving corresponding sets of linear equations. They exploit cache memory by using the block hybrid ... authors in a companion article. The matrix is packed into n(n + 1)/2 real ... subroutines for rearranging a matrix whose upper or lower-triangular part is packed by columns...
• # QR Decomposition

• Referenced in 1 article [sw28565]
• algorithm to decompose a real matrix A into the product of two other matrices ... orthogonal and R is invertible and upper triangular. The algorithm is useful for the least ... approximation of an unsolvable system of linear equations. As a side-product, the Gram-Schmidt...