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Adaptive mesh refinement (AMR) changes the spacing of grid points, to change how accurately the solution is known in that region. In the shallow water example, the grid might in general be spaced every few feet—but it could be adaptively refined to have grid points every few inches in places where there are large waves.
MATLAB does include standard for and while loops, but (as in other similar applications such as APL and R), using the vectorized notation is encouraged and is often faster to execute. The following code, excerpted from the function magic.m , creates a magic square M for odd values of n (MATLAB function meshgrid is used here to generate square ...
The test functions used to evaluate the algorithms for MOP were taken from Deb, [4] Binh et al. [5] and Binh. [6] The software developed by Deb can be downloaded, [7] which implements the NSGA-II procedure with GAs, or the program posted on Internet, [8] which implements the NSGA-II procedure with ES.
A mesh need not be simplicial because an arbitrary subset of nodes of a cell is not necessarily a cell: e.g., three nodes of a quad does not define a cell. However, two cells intersect at cells: e.g. a quad does not have a node in its interior. The intersection of two cells may be several cells: e.g., two quads may share two edges.
In MATLAB, the function kron (A, B) is used for this product. These often generalize to multi-dimensional arguments, and more than two arguments. In the Python library NumPy, the outer product can be computed with function np.outer(). [8] In contrast, np.kron results in a flat array.
By virtue of the linearity property of optical non-coherent imaging systems, i.e., . Image(Object 1 + Object 2) = Image(Object 1) + Image(Object 2). the image of an object in a microscope or telescope as a non-coherent imaging system can be computed by expressing the object-plane field as a weighted sum of 2D impulse functions, and then expressing the image plane field as a weighted sum of the ...
A training data set is a data set of examples used during the learning process and is used to fit the parameters (e.g., weights) of, for example, a classifier. [9] [10]For classification tasks, a supervised learning algorithm looks at the training data set to determine, or learn, the optimal combinations of variables that will generate a good predictive model. [11]
In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-semidefinite. The conjugate gradient method is often implemented as an iterative algorithm , applicable to sparse systems that are too large to be handled by a direct ...