Concepts inSoftware for estimating sparse Jacobian matrices
Jacobian matrix and determinant
In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector- or scalar-valued function with respect to another vector. Suppose F : R ¿ R is a function from Euclidean n-space to Euclidean m-space. Such a function is given by m real-valued component functions, F1(x1,... ,xn), ... , Fm(x1,... ,xn).
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Sparse matrix
In the subfield of numerical analysis, a sparse matrix is a matrix populated primarily with zeros. The term itself was coined by Harry M. Markowitz. Conceptually, sparsity corresponds to systems which are loosely coupled. Consider a line of balls connected by springs from one to the next; this is a sparse system. By contrast, if the same line of balls had springs connecting each ball to all other balls, the system would be represented by a dense matrix.
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