Mathematical software

DiffSharp
Referenced in 25 articles [sw16033]
algorithmic control flow. Using the DiffSharp library, differentiation (gradients, Hessians, Jacobians, directional derivatives, and matrix ... free Hessian- and Jacobian-vector products) is applied using higher-order functions, that is, functions...

pTatin3D
Referenced in 9 articles [sw27642]
driven by buoyancy and processes at the free surface. Geodynamic phenomena such as subduction ... performance and algorithmic tradeoffs of pTatin3D’s multigrid preconditioner. Our matrix-free geometric multigrid preconditioner...

LSTRS
Referenced in 28 articles [sw04729]
Algorithm 873: LSTRS: MATLAB software for large-scale trust-region subproblems and regularization A MATLAB ... problem at each step. LSTRS relies on matrix-vector products only ... computations. In the MATLAB implementation, the Hessian matrix of the quadratic objective function ... matrix-vector multiplication routine. Therefore, the implementation preserves the matrix-free nature of the method...

EVSL
Referenced in 5 articles [sw27222]
matrix-free modes, whereby the user can supply his/her own functions to perform matrix-vector ... sparse linear systems. The paper describes the algorithms in EVSL, provides details on their implementations...

SPRAL
Referenced in 3 articles [sw13035]
algorithms. SSIDS: Sparse Symmetric Indefinte Direct Solver. Requires an NVIDIA GPU! SSMFE: Sparse Symmetric Matrix ... Free Eigensolver. Uses Jacobi-conjugate preconditioned gradients method...

Exa-Dune
Referenced in 10 articles [sw32962]
have developed, implemented and optimised numerical algorithms and software for the scalable solution of partial ... included GPU-based sparse approximate inverses, matrix-free sum-factorisation for high-order discontinuous Galerkin ... discretisations as well as partially matrix-free preconditioners. On top of that, additional scalability ... multiscale methods and the multilevel Monte-Carlo algorithm. Finally, some of the concepts are applied...

Dendro
Referenced in 7 articles [sw29068]
octree forests. We describe a bottom-up algorithm for constructing the coarser multigrid levels ... multigrid sweeps. Also, we describe matrix-free implementations for the discretized PDE operators...

PolyTop++
Referenced in 2 articles [sw17735]
language and the CUDA model to design algorithms with efficient memory management, capable of solving ... iterative solvers, and an iterative ‘matrix-free’ solver; these were all implemented in serial...

DiffSharp