Question

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explain transpose of sparse matrix.............


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Answer 1

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In computer programming, a matrix can be defined with a 2-dimensional array. ... There may be a situation in which a matrix contains more number of ZERO values than NON-ZERO values. Such matrix is known as sparse matrix. Sparse matrix is a matrix which contains very few non-zero elements.

By ℳubashera❤

Answer 2

Step-by-step explanation:

While processor manufacturers repeatedly emphasize the importance of their latest innovations such as vector extensions (AVX, AVX2, etc.) of the processing elements, proper placement of data in memory is at least equally important. At the same time, generic implementations of many different data structures allow one to (re)use the most appealing one quickly. However, the intuitively most appropriate data structure may not be the fastest.

Let us consider the transposition of a sparse matrix A. Such an operation shows up in algebraic multigrid methods for forming the restriction operator from the prolongation operator, or in graph algorithms to obtain neighborhood information. A only has a small number of nonzero entries per row, but can have millions of rows and columns. Clearly, a dense storage of A in a single array is inappropriate, because almost all memory would be wasted for storing redundant zeros. Most practical implementations use a row- or column-oriented storage of A, where for each row (or column) the index and the value of each entry is stored. A simple way of transposing a sparse matrix is to reinterpret a row-oriented storage of A as column-oriented (or vice versa), but we will consider an explicit transposition of matrix A in row-oriented storage into a matrix B=AT with row-oriented storage. Any results obtained subsequently will hold true for the case of column-oriented storage as well.