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In the mathematical discipline of numerical linear algebra, a matrix splitting is an expression which represents a given matrix as a sum or difference of matrices. Many iterative methods (for example, for systems of differential equations) depend upon the direct solution of matrix equations involving matrices more general than tridiagonal matrices.
1.2.0 6 November 2018: Free GPL v.3 or later FOSS statistics program, intended as an alternative to IBM SPSS Statistics. [Note 2] R: R Foundation 1997 1997 4.3.2 31 October 2023: Free GPL: Primarily for statistics, but there are many interfaces to open-source numerical software SageMath: William Stein: 2005 10.2 3 December 2023: Free GPL
MATLAB (an abbreviation of "MATrix LABoratory" [18]) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.
FEATool Multiphysics is a fully integrated physics and PDE simulation environment where the modeling process is subdivided into six steps; preprocessing (CAD and geometry modeling), mesh and grid generation, physics and PDE specification, boundary condition specification, solution, and postprocessing and visualization.
Simulink is a MATLAB-based graphical programming environment for modeling, simulating and analyzing multidomain dynamical systems.Its primary interface is a graphical block diagramming tool and a customizable set of block libraries.
For many problems, relaxing the equality of split variables allows the system to be broken down, enabling each subsystem to be solved separately. This significantly reduces computation time and memory usage. Solving the relaxed problem with variable splitting can give an approximate solution to the initial problem.
The Hopkinson pressure bar was first suggested by Bertram Hopkinson in 1914 [1] as a way to measure stress pulse propagation in a metal bar. Later, in 1949 Herbert Kolsky [2] refined Hopkinson's technique by using two Hopkinson bars in series, now known as the split-Hopkinson bar, to measure stress and strain, incorporating advancements in the cathode ray oscilloscope in conjunction with ...
In numerical linear algebra, the alternating-direction implicit (ADI) method is an iterative method used to solve Sylvester matrix equations.It is a popular method for solving the large matrix equations that arise in systems theory and control, [1] and can be formulated to construct solutions in a memory-efficient, factored form.