Michiel Hochstenbach
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(m.e.hochstenbach tue nl)

Some numerical software (Numerical Linear Algebra, Numerical Mathematics)

Contents:
Numerical linear algebra
Eigenvalue problems
Jacobi-Davidson
Lanczos
Pseudospectra
SVD
Linear systems
LU
Matlab
Sparse matrices
ODE
PDE
FFT
Finite element
Model reduction
Interval arithmetic
Optimization
Symbolic
AMG
Various / Other

Overview

Freely available software for linear algebra on the web
GAMS Guide to Available Mathematical Software

Numerical linear algebra

Trilinos, Parallel Linear Algebra Packages
FLAME, Formal Linear Algebra Methods Environment
      an infrastructure for developing dense (including banded) linear algebra libraries for sequential and multithreaded architectures. It includes an implementation of the BLAS and "core LAPACK".
LAPACK, Linear Algebra PACKage
Netlib linear algebra
Fortran linear algebra
Matrix Computation Toolbox

Eigenvalue problems

Programmed by Michiel Hochstenbach and/or coauthors
Please contact me via (m.e.hochstenbach tue nl) if you are interested
Jacobi-Davidson
Jacobi-Davidson for the singular value problem (JDSVD) (Matlab)
Two-sided Jacobi-Davidson
Alternating Jacobi-Davidson
Jacobi-Davidson for the complex symmetric eigenvalue problem
Jacobi-Davidson for the multiparameter eigenvalue problem


Jacobi-Davidson
The Jacobi-Davidson Gateway
JDQR, for standard eigenvalue problems (Sleijpen) (Matlab)
JDQZ, for generalized eigenvalue problems (Sleijpen) (Matlab)
JADAMILU, for Hermitian (generalized) eigenvalue problems (Bollhöfer, Notay) (Fortran 77)


Lanczos
Lanczos (Cullum and Willoughby) (Fortran)
PROPACK, symmetric eigenvalue problem and singular value problem (Rasmus Munk Larsen) (Matlab, Fortran)


Arnoldi
ARPACK Implicitly restarted Arnoldi (Lehoucq, Maschhoff, Sorensen, Yang) (Fortran)


Various methods
SLEPc, Scalable Library for Eigenvalue Problem Computations
     a parallel software library for the solution of large sparse eigenvalue problems on parallel computers.


Pseudospectra
Matlab GUI for pseudospectra (Wright) (Matlab)


SVD
SVDPACK (Berry) (Fortran)
PROPACK, symmetric eigenvalue problem and singular value problem (Rasmus Munk Larsen) (Matlab, Fortran)

Linear systems

BiCGStab(l): here or here (Matlab, Fortran)
GMRESR (Fortran)
IDR
LINSOL linear equation solver
PARDISO, Parallel Direct Solver for sparse symmetric/nonsymmetric linear systems
ITSOL, a package for solving linear systems of equations by iterative methods (Saad) (C)
KKTDirect, a direct solver for saddle-point matrices
ILUPACK, multilevel ILU preconditioners (Bollhöfer)
pARMS, parallel Algebraic Recursive Multilevel Solver


LU
UMFPACK (sparse LU)
AMD (ordering sparse matrices prior to Cholesky/LU factorization

Matlab and alternatives

SciLab (free "Matlab clone")
Octave (free "Matlab clone")
SageMath ("free open source alternative to Magma, Maple, Mathematica and Matlab")
RLab
Matlab resources
Iterative Methods for Linear and Nonlinear Equations (Kelley) (Matlab)
Matlab Database
Mathtools
Matlab central

Sparse matrices

Matrix Market
SPARSKIT, a basic tool-kit for sparse matrix computations (Saad) (Fortran)
Tools for and sets of sparse matrices
Sparse matrix file format converter
SPAI, SParse Approximate Inverse
Mondriaan, Sparse matrix partitioning package (Bisseling) (C)

QR

SuiteSparseQR, sparse multifrontal QR factorization package

Matrix functions

Matrix Function Toolbox (Higham) (Matlab)
Expokit (Sidje) (Matlab, Fortran)

Tools

TTH, the TEX to HTML translator

ODE, DAE

ODE-IVP, blended implicit methods
BiMD, a variable order-variable stepsize "blended" implicit method for the numerical solution of linearly implicit DAE-IVPs
Test Set for IVP Solvers

PDE

PHAML (Parallel Hierarchical Adaptive MultiLevel) for the solution of second order linear elliptic PDEs (Fortran)
CONCEPTS, a C++ class library for solving elliptic PDEs numerically
Java ODE/PDE routines
Wavelet solvers for PDE and integral equations
PLTMG, a package for solving elliptic partial differential equations in general regions of the plane
PETSc, the Portable Extensible Toolkit for Scientific Computation
     parallel software libraries for the implicit solution of PDEs and related problems involving sparse matrices.
DUNE, modular toolbox for solving partial differential equations (PDEs) with grid-based methods.
     Supports the easy implementation of methods like Finite Elements (FE), Finite Volumes (FV), and Finite Differences (FD).

FFT

NFFT, Nonequispaced Fast Fourier Transform
NDFT, Nonequispaced Discrete Fourier Transform
Fortran subroutine library of Fast Fourier Transforms
Discrete Fourier transform

Finite Element

OpenFEM, an opensource finite element toolbox for Matlab
Getfem++, C++ library for finite element methods elementary computations
SOFEA, Object oriented finite element toolkit
Model Reduction for Finite Elements
IMTEK Mathematica Supplement (focus on Finite Element Computations)
GeoFEM
Deal.II, object-oriented finite element library
iFEM3D, three dimensional version of iFEM three dimensional local refinement of tetrahedron meshes and other components of adaptive finite element methods

Model reduction

Oberwolfach Model Reduction Benchmark Collection

Interval arithmetic

INTLAB Matlab toolbox for interval arithmetic

Optimization

HIFOO, a MATLAB package for H-infinity Fixed Order Optimization
GloptiPoly, moments, optimization and semidefinite programming
ASA_CG, Bound constrained optimization
CVX, MATLAB-based modeling package for disciplined convex programming
NSIPS, Nonlinear Semi-Infinite Programming Solver

Symbolic

MuPad (free "Maple clone")
Chebfun, computation with the feel of symbolics and the speed of numerics
Maxima, a Computer Algebra System

Multigrid

AMG Toolbox (cullumj@lanl.gov)
PyAMG, Algebraic Multigrid Solvers in Python

Latex

Lyx, package for generating LaTeX based documents

C

routines for numerical computing in C

Fortran

Fortranlib

Java

JPM (sparse matrix library for Java)

Graph

SCOTCH, graph, mesh and hypergraph partitioning, static mapping, and sparse matrix block ordering.

Various / Other useful links

SciPy, NumPy, Scientific Tools for Python
MathPlotLib, python 2D plotting library
R, statistical computing
SageMath, open-source mathematics software system
Euler Math Toolbox, software for numerical and symbolic computations
GNU Scientific Library
Numerical Computing Resources
Sources of software
Sandia software
Netlib, for LAPACK, EISPACK, LINPACK and much more
Stanford software
LibMultiScale, a C++ parallel framework for the multiscale coupling methods dedicated to material simulations
MWrap, a tool for generating MATLAB and Octave interfaces to C/C++ code
Semtex, a classical/nodal spectral-element/Fourier code that will solve time-varying incompressible Navier-Stokes problems in 2D or 2+1/2D domains, both Cartesian and cylindrical.
El Topo, public domain C++ package for tracking dynamic surfaces in 3D represented with triangle meshes
SeDuMi,
Computational Convex Analysis (CCA) numerical library, numerical computation of fundamental convex transforms arising from Convex Analysis using hybrid symbolic-numeric algorithms.
FLAP, A Matlab Package for Adjustable Floating-Point Arithmetic (Stewart)
CADNA, estimate the accuracy of a computed result
High Performance Linpack
MLD2P4, Fortran 95 package of parallel multilevel preconditioners
MOORe Tools, Modular Object-Oriented Regularization Tools (Hansen)
Regularization Tools (Hansen)
VERSOFT, Verification software in MATLAB, including verified eigenvalues and eigenvectors
LSMLIB, Level Set Method Library, serial and parallel simulation of implicit surface and curve dynamics in two and three dimensions.
Sollya, a general tool supporting the synthesis of numerical codes, including a (multiprecision) infinite norm algorithm for univariate functions, best polynomial approximation of a function.
TetGen, A Tetrahedral Mesh Generator and 3D Delaunay Triangulator
The GNU Scientific Library
A Toolbox of Level Set Methods
Term Document Generator for MATLAB
Curvelab, toolbox implementing the Curvelet transform
Fortran 90 code for Second Order Problems
MUMPS, MUltifrontal Massively Parallel Solver
Transactions on Mathematical Software
Numerical Recipes Software's Books On-Line
Dundee Software Links, LaTeX, Maple, Matlab, Finite elements, mesh generation
Numerical Recipes
Harwell Subroutine Library
CADNA, Control of Accuracy and Debugging for Numerical Appplications
Matlab Differentiation Matrix Suite
TraFlowPACK
SLICOT Control Software
Acrobat reader


Commercial

The Mathworks
NAG Numerical Software
Numeritek Website
NMath Matrix
TOMLAB, nonlinear optimization in Matlab
Math Kernel Library, math routines for science, engineering, and financial application
WSMP, Watson Sparse Matrix Package

Michiel Hochstenbach
Email: (m.e.hochstenbach tue nl)