sparse matrix

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sparse matrix A matrix usually arising in the context of linear algebraic equations of the form Ax = b in which A is of large order and has a high proportion of zero elements (greater than, say, 90%). Special techniques are available that exploit the large number of zeros and reduce considerably the computational effort when compared to a general full matrix. Examples of such methods are variants of Gaussian elimination (see linear algebraic equations) and iteration methods. Large sparse systems can arise in the numerical solution of ordinary and partial differential equations. See also numerical linear algebra.