• Algorithm 432

  • Referenced in 252 articles [sw25817]
  • Algorithm 432: Solution of the matrix equation AX + XB = C [F4]. The following programs ... Fortran IV subroutines to solve the matrix equation AX+XB=C(1) where...
  • LAPACK

  • Referenced in 1702 articles [sw00503]
  • systems of equations, eigenvalue problems, and singular value problems. The associated matrix factorizations (LU, Cholesky...
  • PETSc

  • Referenced in 1584 articles [sw04012]
  • expanding suite of parallel linear, nonlinear equation solvers and time integrators that may be used ... within parallel application codes, such as parallel matrix and vector assembly routines. The library...
  • ScaLAPACK

  • Referenced in 418 articles [sw00830]
  • equations, condition estimation and iterative refinement, for LU and Cholesky factorization, matrix inversion, full-rank...
  • LMI toolbox

  • Referenced in 1463 articles [sw06383]
  • Linear Matrix Inequalities (LMIs) and LMI techniques have emerged as powerful design tools in areas ... than that of solving, say, a Riccati equation. For instance, problems with a thousand design...
  • REDUCE

  • Referenced in 746 articles [sw00789]
  • solution of a variety of algebraic equations; facilities for the output of expressions ... wide variety of special functions; Dirac matrix calculations of interest to high energy physicists...
  • MESS

  • Referenced in 30 articles [sw14886]
  • E.S.S, Matrix Equation Sparse Solvers (MESS): A MATLAB Toolbox for the Solution of Sparse Large ... Scale Matrix Equations. MESS is the successor to the LyaPack Toolbox for MATLAB ... intended for solving large sparse matrix equations. The new version has been rewriten in large...
  • Expokit

  • Referenced in 200 articles [sw00258]
  • full, the action of a large sparse matrix exponential on an operand vector ... differential equations with constant inhomogeneity. The backbone of the sparse routines consists of matrix-free...
  • glasso

  • Referenced in 457 articles [sw07432]
  • glasso can be tricky; the converged precision matrix might not be the inverse ... outperform glasso. By studying the “normal equations” we see that, glasso is solving the dual ... target of estimation is Σ, the covariance matrix, rather than the precision matrix...
  • VODE

  • Referenced in 207 articles [sw01005]
  • stiff) systems of ordinary differential equations. The new package can be considered ... Jacobian matrix to be used in the solution of the implicit equations by quasi Newton...
  • LSQR

  • Referenced in 394 articles [sw00530]
  • Algorithm 583: LSQR: Sparse Linear Equations and Least Squares Problems. An iterative method is given ... where the matrix A is large and sparse. The method is based on the bidiagonalization...
  • HOMPACK

  • Referenced in 122 articles [sw05324]
  • curve: ordinary differential equation-based, normal flow, and augmented Jacobian matrix. Separate routines are also...
  • na12

  • Referenced in 29 articles [sw11490]
  • quadratically convergent method for solving the matrix equation X = ∑+ ∞ i=0 Xi Ai, where...
  • CSparse

  • Referenced in 237 articles [sw20382]
  • solution of sparse systems of linear equations. Attacking these problems efficiently requires an in-depth ... algorithms, and data structures found in sparse matrix software libraries. Here, Davis presents the fundamentals...
  • Polynomial Toolbox

  • Referenced in 33 articles [sw07237]
  • symmetric polynomial equations with complex coefficients are studied in the scalar and matrix case ... study theoretical properties of the equations. Sylvester matrix algorithms are then developed to solve numerically...
  • BiCGstab

  • Referenced in 128 articles [sw04022]
  • linear algebraic equations with a non-singular n×n matrix are studied. The basis...
  • YSMP

  • Referenced in 73 articles [sw17947]
  • Sparse Matrix Package (YSMP). The Yale sparse matrix package is a collection of routines ... system of linear equations Mx=b when the coefficient matrix M is large and sparse...
  • Quantomatic

  • Referenced in 22 articles [sw10107]
  • graphical relationships via the unification of matrix equations. Since these equations can grow exponentially with...
  • SCASY

  • Referenced in 12 articles [sw03251]
  • parallel algorithms for Sylvester-type matrix equations with some applications In this contribution, we review ... time and discrete-time Sylvester-type matrix equations. The analysis is based on RECSY ... ways of introducing blocking for solving matrix equations in reduced (quasi-triangular) form are reviewed ... consider parallelization of algorithms for reduced matrix equations at two levels: globally in a distributed...