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Matrix-free conjugate gradient method has been applied in the non-linear elasto-plastic finite element solver. [7] Solving these equations requires the calculation of the Jacobian which is costly in terms of CPU time and storage. To avoid this expense, matrix-free methods are employed.
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.
FreeMat is a free open-source numerical computing environment and programming language, [1] similar to MATLAB and GNU Octave. [2] In addition to supporting many MATLAB functions and some IDL functionality, it features a codeless interface to external C, C++, and Fortran code, further parallel distributed algorithm development (via MPI), and has plotting and 3D visualization capabilities. [3]
The first step when using the direct stiffness method is to identify the individual elements which make up the structure. Once the elements are identified, the structure is disconnected at the nodes, the points which connect the different elements together.
In the first step we distribute the input matrices between the processors based on the previous rule. In the next iterations we choose a new k' := (k + 1) mod n for every processor. This way every processor will continue accessing different values of the matrices. The needed data is then always at the neighbour processors.
The Free-orbit Experiment with Laser Interferometry X-Rays (FELIX) [1] belongs to a category of experiments exploring whether macroscopic systems can be in superposition states.
The basic eight-point algorithm is here described for the case of estimating the essential matrix .It consists of three steps. First, it formulates a homogeneous linear equation, where the solution is directly related to , and then solves the equation, taking into account that it may not have an exact solution.
This is the normalization used by Matlab, for example, see. [99] In many applications, such as JPEG, the scaling is arbitrary because scale factors can be combined with a subsequent computational step (e.g. the quantization step in JPEG [100]), and a scaling can be chosen that allows the DCT to be computed with fewer multiplications. [101] [102]