• # LAPACK

• Referenced in 1713 articles [sw00503]
• problems, and singular value problems. The associated matrix factorizations (LU, Cholesky, QR, SVD, Schur, generalized ... factorizations and estimating condition numbers. Dense and banded matrices are handled, but not general sparse ... reorganizing the algorithms to use block matrix operations, such as matrix multiplication, in the innermost...
• # ScaLAPACK

• Referenced in 421 articles [sw00830]
• includes routines for the solution of dense, band, and tridiagonal linear systems of equations, condition ... iterative refinement, for LU and Cholesky factorization, matrix inversion, full-rank linear least squares problems...
• # CVODE

• Referenced in 65 articles [sw04947]
• direct linear solver (dense or banded), the Newton iteration is a Modified Newton iteration ... Newton iteration, using the current Jacobian (through matrix-free products), in which the linear residual ... module, CVODE provides both direct (dense and band) solvers and three preconditioned Krylov (iterative) solvers...
• # FIDE

• Referenced in 5 articles [sw09196]
• difference schemes. CHARPOL for calculating the amplification matrix and characteristic polynomial of difference schemes, which ... system of linear algebraic equations with band matrix appearing frequently in difference schemes. The FIDE...
• # NAPACK

• Referenced in 71 articles [sw11666]
• matrix by a vector, to invert a matrix, to solve least squares problems, to perform ... package has special routines for general, band, symmetric, indefinite, tridiagonal, upper Hessenberg, and circulant matrices...
• # VODE

• Referenced in 214 articles [sw01005]
• possibility to save the Jacobian matrix to be used in the solution of the implicit ... Jacobian is banded in all cases. It is found that the run time is reduced...
• # LASO2

• Referenced in 3 articles [sw28488]
• eigenvalues of a large (sparse) symmetric matrix. The LASO package is documented in a technical ... compute the eigenvalues of the band matrix generated by the Lanczos algorithm. It also monitors...
• # FEAST

• Referenced in 92 articles [sw04025]
• algorithm takes its inspiration from the density-matrix representation and contour integration technique in quantum ... ready to use predefined interfaces for dense, banded and sparse systems. It includes double...
• # ggb

• Referenced in 1 article [sw31338]
• Graph-guided banding of the covariance matrix. Regularization has become a primary tool for developing ... that the population covariance (or inverse covariance) matrix is sparse, while making no particular structural ... known ordering, in which case a banded population matrix is often assumed. While the banded...
• # Algorithm 923

• Referenced in 6 articles [sw20231]
• banded skew-symmetric matrices. Computing the Pfaffian of a skew-symmetric matrix is a problem ... solved easily once the skew-symmetric matrix has been reduced to skew-symmetric tridiagonal form ... rotations, that are applicable to dense and banded matrices, respectively. We also give a complete ... based on the Hamiltonian and the scattering matrix...
• # SBR Toolbox

• Referenced in 21 articles [sw10146]
• reduction of banded matrices to narrower banded or tridiagonal form, with optional accumulation ... codes to particular machine and matrix characteristics. We also briefly describe the testing and timing...
• # hierband

• Referenced in 1 article [sw31337]
• package hierband: Convex Banding of the Covariance Matrix. Implementation of the convex banding procedure (using ... Bien, Bunea, Xiao (2015) Convex Banding of the Covariance Matrix. Accepted for publication in JASA...
• # PaFiBo-OBGAIM

• Referenced in 2 articles [sw19565]
• explicit finite difference (FD) approximate inverse matrix methods, based on Portable Operating System Interface ... systems. Parallelization of the Optimized Banded Generalized Approximate Inverse Matrix (OBGAIM) algorithm is achieved based ... different index bands and with proper synchronization points on inner products and matrix-vector multiplications...
• # PEPBICG-STAB

• Referenced in 2 articles [sw19566]
• explicit finite difference (FD) approximate inverse matrix methods, based on Portable Operating System Interface ... systems. Parallelization of the Optimized Banded Generalized Approximate Inverse Matrix (OBGAIM) algorithm is achieved based ... different index bands and with proper synchronization points on inner products and matrix-vector multiplications...