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The General Problem Solver (GPS) is a particular computer program created in 1957 by Herbert Simon, J. C. Shaw, and Allen Newell intended to work as a universal problem solver, that theoretically can be used to solve every possible problem that can be formalized in a symbolic system, given the right input configuration.
Popular solver with an API (C, C++, Java, .Net, Python, Matlab and R). Free for academics. Excel Solver Function: A nonlinear solver adjusted to spreadsheets in which function evaluations are based on the recalculating cells. Basic version available as a standard add-on for Excel. GAMS: A high-level modeling system for mathematical optimization ...
Lis is a scalable parallel library for solving systems of linear equations and eigenvalue problems using iterative methods. Intel MKL (Math Kernel Library) contains optimized math routines for science, engineering, and financial applications, and is written in C/C++ and Fortran. Core math functions include BLAS, LAPACK, ScaLAPACK, sparse ...
TK Solver is a mathematical modeling and problem-solving software system based on a declarative, rule-based language, commercialized by Universal Technical Systems, Inc. Torch is a deep-learning library with support for manipulation, statistical analysis and presentation of Tensors.
API to MATLAB and Python. Solve example Linear Programming (LP) problems through MATLAB, Python, or a web-interface. CPLEX: Popular solver with an API for several programming languages, and also has a modelling language and works with AIMMS, AMPL, GAMS, MPL, OpenOpt, OPL Development Studio, and TOMLAB. Free for academic use. Excel Solver Function
Excel maintains 15 figures in its numbers, but they are not always accurate; mathematically, the bottom line should be the same as the top line, in 'fp-math' the step '1 + 1/9000' leads to a rounding up as the first bit of the 14 bit tail '10111000110010' of the mantissa falling off the table when adding 1 is a '1', this up-rounding is not undone when subtracting the 1 again, since there is no ...
The implementation of this method in the free software MPSolve is a reference for its efficiency and its accuracy. Another method with this style is the Dandelin–Gräffe method (sometimes also ascribed to Lobachevsky), which uses polynomial transformations to repeatedly and implicitly square the roots. This greatly magnifies variances in the ...
In contrast, direct methods attempt to solve the problem by a finite sequence of operations. In the absence of rounding errors , direct methods would deliver an exact solution (for example, solving a linear system of equations A x = b {\displaystyle A\mathbf {x} =\mathbf {b} } by Gaussian elimination ).