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: Numerical Analysis
Learn the Art of Computer Programming With These Great Free Beginner Books
Learning to code still remains a buzz. The problem facing any budding new programmer is how to start. Questions abound. What's the best programming language for a beginner? What's the best way to learn? A beginner might be tempted by reading books titled 'teach yourself [insert programming language] in 24 hours'. But don't be in such a rush. In my opinion, it is best to first get interested in programming, then seek out some experienced coders and discuss and discuss, and learn programming by doing, practising with lots of practical examples and the aid of an excellent introductory book.
(Read more)
Graphviz
Graphviz is open source graph visualization software. It has several main graph layout programs. It also has web and interactive graphical interfaces, and auxiliary tools, libraries, and language bindings.
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GAUSS
(commercial) An easytouse data analysis, mathematical and statistical environment based on the powerful, fast and efficient GAUSS Matrix Programming Language. GAUSS is used to solve real world problems and data analysis problems of exceptionally large scale.
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Octave
GNU Octave is a highlevel language, primarily intended for numerical computations. It provides a convenient command line interface for solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with Matlab. It may also be used as a batchoriented language. Octave has extensive tools for solving common numerical linear algebra problems, finding the roots of nonlinear equations, integrating ordinary functions, manipulating polynomials, and integrating ordinary differential and differentialalgebraic equations. It is easily extensible and customizable via userdefined functions written in Octave's own language, or using dynamically loaded modules written in C++, C, Fortran, or other languages.
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AcouSTO
AcouSTO (Acoustics Simulation TOol) is an open source Boundary Element Method (BEM) solver for the KirchhoffHelmholtz Integral Equation (KHIE). An arbitrary number of scattering bodies, sources, and plane waves is allowed.
ADMesh
ADMesh is a program for processing triangulated solid meshes. Currently, ADMesh only reads the STL file format that is used for rapid prototyping applications, although it can write STL, VRML, OFF, and DXF files.
Aladdin
a Computational Toolkit for Interactive Engineering Matrix and Finite Element Analysis
ALBERT
ALBERTA is an Adaptive multiLevel finite element toolbox using Bisectioning refinement and Error control by Residual Techniques for scientific Applications.
Algae
Algae is a programming language for numerical analysis. Algae was developed because we needed a fast and versatile tool, capable of handling large systems. Algae has been applied to interesting problems in aerospace and related fields for more than a decade.
AMESH
(commercial) a series of mesh generation tools designed specifically for the casting industry. AMESH uses a unique meshing method to construct multicomponent (casting, mold, core, chill, etc.) geometry simultaneously. This ensures an accurate finite element model which is representative of the problem at hand
ATLAS
Automatically Tuned Linear Algebra Software: an approach for the automatic generation and optimization of numerical software for processors with deep memory hierarchies and pipelined functional units
BLOPEX
BLOPEX is a package, written in C, that at present includes only one eigenxolver, Locally Optimal Block Preconditioned Conjugate Gradient Method (LOBPCG). BLOPEX supports parallel MPIbased computations. The complex arithmetic is not yet supported in BLOPEX C codes, but is available for MATLAB codes.
Blossom IV
Blossom IV is a minimum weight perfect matchings for pointsets in two or three dimensions with different norms as well as matchings for graphs given by a distance matrix.
BoxLib
BoxLib is a library of C++ classes that facilitate the development of block structured finite difference algorithms such as arise in the solution of systems of partial differential equations. BoxLib is particularly useful in designing and building adaptive algorithms. BoxLib contains rich data structures for describing operations which take place on data defined in regions of index space that are unions of nonintersecting rectangles.
Cactus
Cactus is an open source problem solving environment designed for scientists and engineers. Its modular structure easily enables parallel computation across different architectures and collaborative code development between different groups. Cactus originated in the academic research community, where it was developed and used over many years by a large international collaboration of physicists and computational scientists.
CalculiX
CalculiX is a package designed to solve field problems. The method used is the finite element method. With CalculiX Finite Element Models can be build, calculated and postprocessed. The pre and postprocessor is an interactive 3Dtool using the openGL API. The solver is able to do linear and nonlinear calculations. Static, dynamic and thermal solutions are available.
CAP
(commercial) CAP is a 3D finite element analysis program that simulates solidification processes. CAP can be used on various casting processes, different mold materials, and multiple casting materials. CAP can also be used to optimize casting geometry in order to improve part integrity and reduce costs.
Cart3d
Cart3D is a highfidelity inviscid analysis package for conceptual and preliminary aerodynamic design. It allows users to perform automated CFD analysis on complex geometry. The package includes utilities for geometry import, surface modeling and intersection, mesh generation and flow simulation. Currently the package includes two flow simulation codes, Tiger, and flowCart.
Cassowary
Cassowary is an incremental constraint solving toolkit that efficiently solves systems of linear equalities and inequalities. Constraints may be either requirements or preferences. Client code specifies the constraints to be maintained, and the solver updates the constrained variables to have values that satisfy the constraints.
CastCAE
(commercial) CastCAE is the tool for foundries interested in casting simulation. CastDESIGN is a revolutionary simulation package that helps in designing the feeding systems for your castings. With CastCHECK, every machine designer can check and improve the castability of the components without extensive foundry knowledge.
Cheap Matrix
Cheap Matrix is a C++ Matrix class optimized for memory before speed. It enables handling huge matrices, and can link with LAPACK.
CLUTO
CLUTO is a software package for clustering low and highdimensional datasets and for analyzing the characteristics of the various clusters. CLUTO is wellsuited for clustering data sets arising in many diverse application areas including information retrieval, customer purchasing transactions, web, GIS, science, and biology.
CSCMDO
The Coordinate and Sensitivity Calculator for Multidisciplinary Design Optimization CSCMDO is a general purpose multiblock threedimensional volume grid generator which is suitable for Multidisciplinary Design Optimization.
CSDP
CSDP is a library of routines that implements a predictor corrector variant of the semidefinite programming algorithm of Helmberg, Rendl, Vanderbei, and Wolkowicz.
diffpack
(commercial) consists of a collection of objectoriented libraries (implemented in C++) for solving partial differential equations with a particular focus on finite element methods, and several Unix utilities for general software management and numerical programming
dstool tk
dstool tk is a dynamical systems toolkit. It's very useful in the visual study of nonlinear systems and Chaos, as well as for finding numerical solutions to differential equations.
DUNE
DUNE, the Distributed and Unified Numerics Environment, is a modular toolbox for solving partial differential equations (PDEs) with gridbased methods. DUNE is first of all a set of abstract interfaces which embody concepts from scientific computing.
FEATFLOW
FEATFLOW is both a user oriented as well as a general purpose subroutine system for the numerical solution of the incompressible NavierStokes equations in two and three space dimensions.
FEMSET
FEMSET is a library of FEM routines.
FLOW3D
(commercial) FLOW3D is a general purpose CFD software package capable of simulating a wide variety of fluid flows.
FreeFEM
FreeFEM is an implementation of the Gfem language dedicated to the finite element method. It provides you a way to solve Partial Differential Equations (PDE) simply.
gridpak
gridpak is a program which creates an orthogonal grid when provided with the boundary information. The other programs in gridpak are support for this program and do such things as aid in the defining of the grid boundary or finding the bathymetry on the finished grid.
GSL shell
GSL shell is an interactive command line interface that gives easy access to the GNU Scientific Library (GSL) collection of mathematical methods for numerical computations.
GUST
GUST is an unstructured grid generator, flow analysis code, graphical user interfaces, and postprocessing utilities.
HASAS
HydroAcoustic Signal Analysis System: a modular system for passive sonar signal analysis. It can be used for biological research or surveillance
HOPSPACK
HOPSPACK solves derivativefree optimization problems in a C++ software framework. The framework enables parallel operation using MPI (for distributed machine architectures) and multithreading (for single machines with multiple processors or cores).
HQP
HQP is a solver for nonlinearly constrained largescale optimization. It is intended for problems with sufficient regular sparsity structure, e.g. multistage problems, discretetime optimal control problems.
keyFE2
keyFE2 is a FE (finite elements) program devoted to the resolution of discretized partial derivative equations.
KFem
This is a client/server/CORBA software aiming at solving partial differential equations.The server provides the solver while the client provides the input data and the handling of the output using a graphic library, vtk.
KMonodim
KMonodim is a simple solver for monodimensional problems. It provides calculation of eigenvalues and eigenfunctions for a given system, Richardson extrapolation to achieve better precision & integral evaluations.
kOctave
kOctave is a KDE GUI for Octave. kOctave contains a editor with syntax highlighning and a help browser, you can work almost the same way as in Matlab.
LASSPTools
LASSPTools is a collection of Unix utilities for numerical analysis and graphics. It was written around 1990.
levmar
levmar is a robust and efficient C/C++ implementation of the LevenbergMarquardt nonlinear least squares algorithm. It includes double and single precision LM versions, both with analytic and finite difference approximated Jacobians. It also has some support for constrained nonlinear least squares, allowing linear equation and box constraints to be imposed. Availability of LAPACK/BLAS is strongly recommended for carrying out linear algebra computations.
LINDO
(commercial) LINDO is a versatile tool for solving linear, integer, and quadratic programming problems.
mathnium
Mathnium is a program for interactive numerical computations. With its comprehensive library of functions for a variety of problems in applied mathematics, and with its facilities for the definition and manipulation of arrays of numbers as basic data objects, Mathnium allows you to solve numerical problems rather painlessly and without a great deal of programming effort.
MAXDET
MAXDET is an implementation of a longstep pathfollowing method for determinant maximization problems. Includes full Csource (with calls to LAPACK), which can be used directly or via matlab mex file interfaces, matlab examples, and documentation.
MeshMaker
MeshMaker is a comparatively simple program for generating unstructured meshes over a prespecified orography.
METIS
METIS is a set of programs for partitioning graphs, partitioning finite element meshes, and for producing fill reducing orderings for sparse matrices.
MGGHAT
MultiGrid Galerkin Hierarchical Adaptive Triangles: a FORTRAN program for the solution of general second order linear selfadjoint elliptic partial differential equations with Dirichlet, natural or mixed boundary conditions on 2D polygonal domains (possibly with holes)
Mgsor
Mgsor solves the Laplace equation in cartesian coordinates, discretized with the 5point approximation to the derivative.
MODULEF
The MODULEF library contains about 3000 procedures written in Fortran 77. These procedures were designed with the utmost concern for software portability. The approach used in building this library of procedures is a combination of abstract approach and modular programming. By implementing a topdown design, mathematical formulations are split into successive operators.
MOSEK
(commercial) MOSEK is an optimization toolbox for MIDEVA and MATLAB. MOSEK is compatible with a subset of the MathWorks Optimization Toolbox version 2, and includes a muchfaster implementation for linprog, quadprog, lsqnonneg, and lsqlin.
MSC.Patran
(commercial) MSC.Patran provides a complete software environment for companies performing simulation of mechanical products.
MUMPS
MUMPS is a MUltifrontal Massively Parallel sparse direct Solver. It provides a Solution of large linear systems with symmetric positive definite matrices, general symmetric matrices, and general unsymmetric matrices.
MV++
MV++ is a small, efficient, set of concrete vector and simple matrix classes for numerical computing. It is not intended as a general vector container class, but rather designed specifically for optimized numerical computations on RISC and pipelined architectures. It is one step above a C/C++ array.
Nast++
Nast++ is a C++ framework for solving NavierStokes equations with complex geometries (in German).
Octave GTK
A set of GTK+ bindings for Octave, to help develop GUI programs from Octave, with GTK+. It aims to aid fast creation of scientific programs that need GUIs as well as number crunching power.
OPBDP
OPBDP is an implementation in C++ of an implicit enumeration algorithm for solving (non)linear 01 (or pseudoBoolean) optimization problems with integer coefficients.
OpenAxiom
OpenAxiom is an open source platform for symbolic, algebraic, and numerical computations. It offers an interactive environment, an expressive programming language, a compiler, a large set of mathematical libraries of interest to researchers and practitioners of computational sciences.
Orderpack
Orderpack contains public domain Fortran 90 source code for a wide variety of general and specialized ordering problems.
Overture
Overture is an objectoriented code framework for solving partial differential equations. It provides a portable, flexible software development environment for applications that involve the simulation of physical processes in complex moving geometry.
pdelib
pdelib is a collection of software components which are useful to create simulators based on partial differential equations. The main idea of the package is modularity, based on a pattern oriented bottom up design. The user interface is based on the powerful scripting language Lua. Modern 3D graphics hardware output can be utilized for online visualization and generation of MPEG videos.
PDEsim
PDEsim is a Monte Carlo partial differential equation solver.
peakomat
peakomat (former lorentz) is a curve fitting program aimed for fast and easy fitting of spectroscopic data, especially if you face a large amount of similar spectra.
PHAML
PHAML is a parallel program for the solution of 2D elliptic partial differential equations using low or high order finite elements, adaptive mesh refinement based on newest node bisection of triangles, and multigrid. All aspects of the method are based on the hierarchical basis functions.
PPBB
The Portable Parallel BranchandBound Library (PPBBLibrary) presents an easy way to parallelize sequential BranchandBound algorithms for several architectures. A user of the library, who wants to run his sequential algorithm on a parallel system, needs neither knowledge about the hardware architecture nor the parallelization mechanisms.
PVODE
PVODE is a solver for large systems of ordinary differential equations on parallel machines. It contains methods for the solution of both stiff and nonstiff initial value problems.
pysimplex
pysimplex provides some basic symbolic programming tools for constructing, solving and optimizing systems of linear equations and inequalities.
QMG
The QMG package generates finite element meshes in two and three dimensions. QMG is free software distributed at the sourcecode level. Although QMG is free, it is copyrighted by Cornell University. The package includes some geometric modeling software, the mesh generator itself, and an elementary finite element solver. The software is written in C++, Tcl/Tk and Matlab.
radarfdtd
radarfdtd lets you compute the propagation of electromagnetic waves according to Maxwell's equations.
SIMTEC
(commercial) SIMTEC is a FEM based solidification modeling program.
SLFFEA
SLFFEA stands for San Le's Free Finite Element Analysis. It is a package of scientific software and graphical user interfaces for use in finite element analysis. It is written in ANSI C by San Le and distributed under the terms of the GNU license.
Solving Constraint Integer Programs
SCIP is a framework for Constraint Integer Programming oriented towards the needs of Mathematical Programming experts who want to have total control of the solution process and access detailed information down to the guts of the solver. SCIP can also be used as pure MIP solver or as framework for branchcutandprice.
SolvOpt
The program SolvOpt (Solver for local optimization problems) is concerned with minimization or maximization of nonlinear, possibly nonsmooth objective functions and solution of nonlinear minimization problems taking into account constraints by the method of exact penalization.
StarFLIP++
StarFLIP++ is a reusable iterative optimization library for combinatorial problems with fuzzy constraints.
SYMPHONY
SYMPHONY is a fully parallel, generic implementation of the branch, cut, and price algorithm for solving integer and mixedinteger programs. The user of the library need only supply modelspecific preprocessing and separation functions to implement a stateoftheart branch and cut algorithm for virtually any problem setting.
Systems of Ordinary Differential Equations
SODE uses long Taylor series to solve systems of ordinary differential equations. It generates code to solve the equations in either Icon (or Unicon) or Maple. Using the Taylor series, estimates are made of the location and order of poles. An effort is made to adjust H to control the error. It has worked well in testing, but needs more testing as there are so many possibilities.
TeLa
TeLa is a numerical computing environment mainly targeted for numerical simulation pre and postprocessing work.
VBCTOOL
VBCTOOL is a graphical interface for Visualization of Branch Cut algorithms.
Xcog
Xcog is an interactive 2D overlapping grid generator.
XPPAUT
XPPAUT is for the analysis and simulation of dynamic systems. It includes AUTO, a bifurcation package, as well as dozens of other useful routines. Differential equations, maps, stochastic systems, delay equations, integral equations, and other systems are easily solved and plotted.
Zimpl
Zimpl is a little language to translate the mathematical model of a problem into a linear or (mixed) integer mathematical program expressed in .lp or .mps file format which can be read and (hopefully) solved by a LP or MIP solver.
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