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He developed MATLAB's initial linear algebra programming in 1967 with his one-time thesis advisor, George Forsythe. [21] This was followed by Fortran code for linear equations in 1971. [21] Before version 1.0, MATLAB "was not a programming language; it was a simple interactive matrix calculator. There were no programs, no toolboxes, no graphics.
C++ template library; binds to optimized BLAS such as the Intel MKL; Includes matrix decompositions, non-linear solvers, and machine learning tooling Eigen: Benoît Jacob C++ 2008 3.4.0 / 08.2021 Free MPL2: Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms. Fastor [5]
Jblas: Linear Algebra for Java, a linear algebra library which is an easy to use wrapper around BLAS and LAPACK. Parallel Colt is an open source library for scientific computing. A parallel extension of Colt. Matrix Toolkit Java is a linear algebra library based on BLAS and LAPACK. ojAlgo is an open source Java library for mathematics, linear ...
Armadillo is a C++ linear algebra library aiming towards a good balance between speed and ease of use. It employs template classes, and has optional links to BLAS/ATLAS and LAPACK. It is sponsored by NICTA (in Australia) and is licensed under a free license. [47] LAPACK LAPACK is a higher level Linear Algebra library built upon BLAS.
C++ template library for linear algebra; includes various decompositions and factorisations; syntax is similar to MATLAB. GNU Scientific Library: GNU Project C 1996 2.7, 1 June 2021 Free GPL: General purpose numerical analysis library. Targets Linux, can be built on almost any *nix OS with Ansi C compiler. ILNumerics: H. Kutschbach C#, PowerShell
ATLAS runs on most Unix-like operating systems and on Microsoft Windows (using Cygwin). It is released under a BSD-style license without advertising clause, and many well-known mathematics applications including MATLAB, Mathematica, Scilab, SageMath, and some builds of GNU Octave may use it.
Programming languages that implement matrices may have easy means for vectorization. In Matlab/GNU Octave a matrix A can be vectorized by A(:). GNU Octave also allows vectorization and half-vectorization with vec(A) and vech(A) respectively. Julia has the vec(A) function as well.
In numerical linear algebra, the Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a system of linear equations. It is named after the German mathematicians Carl Friedrich Gauss and Philipp Ludwig von Seidel .