10/29/2023 0 Comments Creating a matrix in matlabBy contrast, if the same line of balls were to have springs connecting each ball to all other balls, the system would correspond to a dense matrix. For example, consider a line of balls connected by springs from one to the next: this is a sparse system as only adjacent balls are coupled. The number of zero-valued elements divided by the total number of elements (e.g., m × n for an m × n matrix) is sometimes referred to as the sparsity of the matrix.Ĭonceptually, sparsity corresponds to systems with few pairwise interactions. By contrast, if most of the elements are non-zero, the matrix is considered dense. There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse but a common criterion is that the number of non-zero elements is roughly equal to the number of rows or columns. In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. The non-zero elements are shown in black. Its sparsity is 74%, and its density is 26%.Ī sparse matrix obtained when solving a finite element problem in two dimensions. The above sparse matrix contains only 9 non-zero elements, with 26 zero elements.
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