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A sparse matrix obtained when solving a finite element problem in two dimensions. The non-zero elements are shown in black. In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. [1]
The matrix (typically assumed to be full-rank) is referred to as the dictionary, and is a signal of interest. The core sparse representation problem is defined as the quest for the sparsest possible representation α {\displaystyle \alpha } satisfying x = D α {\displaystyle x=D\alpha } .
Sparse matrix–vector multiplication (SpMV) of the form y = Ax is a widely used computational kernel existing in many scientific applications. The input matrix A is sparse . The input vector x and the output vector y are dense.
A frontal solver is an approach to solving sparse linear systems which is used extensively in finite element analysis. [1] Algorithms of this kind are variants of Gauss elimination that automatically avoids a large number of operations involving zero terms due to the fact that the matrix is only sparse. [2]
In many practical situations, additional information about the matrices involved is known. An important case is sparse matrices, that is, matrices most of whose entries are zero. There are specifically adapted algorithms for, say, solving linear systems Ax = b for sparse matrices A, such as the conjugate gradient method. [46]
librsb is an open-source parallel library for sparse matrix computations using the Recursive Sparse Blocks (RSB) matrix format. librsb provides cache efficient multi-threaded Sparse BLAS operations via OpenMP , and is best suited to large sparse matrices .
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Sparse matrix–vector multiplication; T. Tridiagonal matrix; Z. Zero matrix This page was last edited on 31 December 2018, at 21:40 (UTC). Text is available under ...