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### 21.1 The Creation and Manipulation of Sparse Matrices

The size of mathematical problems that can be treated at any particular time is generally limited by the available computing resources. Both, the speed of the computer and its available memory place limitation on the problem size.

There are many classes of mathematical problems which give rise to matrices, where a large number of the elements are zero. In this case it makes sense to have a special matrix type to handle this class of problems where only the non-zero elements of the matrix are stored. Not only does this reduce the amount of memory to store the matrix, but it also means that operations on this type of matrix can take advantage of the a-priori knowledge of the positions of the non-zero elements to accelerate their calculations.

A matrix type that stores only the non-zero elements is generally called sparse. It is the purpose of this document to discuss the basics of the storage and creation of sparse matrices and the fundamental operations on them.