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Dictionary Meaning and Definition on 'Fill-in'

Fill-in Meaning and Definition from WordNet (r) 2.0
    fill-in n : someone who takes the place of another (as when things get dangerous or difficult); "the star had a stand-in for dangerous scenes"; "we need extra employees for summer fill-ins" [syn: stand-in, substitute, relief, reliever, backup, backup man]
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Wikipedia Meaning and Definition on 'Fill-in'

In the subfield of numerical analysis, a sparse matrix is a matrix populated primarily with zeros (Stoer & Bulirsch 2002, p. 619). 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. The concept of sparsity is useful in combinatorics and application areas such as network theory, which have a low density of significant data or connections.

Huge sparse matrices often appear in science or engineering when solving partial differential equations.

When storing and manipulating sparse matrices on a computer, it is beneficial and often necessary to use specialized algorithms and data structures that take advantage of the sparse structure of the matrix. Operations using standard dense matrix structures and algorithms are slow and consume large amounts of memory when applied to large sparse matrices. Sparse data is by nature easily compressed, and this compression almost always results in significantly less computer data storage usage. Indeed, some very large sparse matrices are infeasible to manipulate with the standard dense algorithms.

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