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In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. [1] 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 ...
Array, a sequence of elements of the same type stored contiguously in memory; Record (also called a structure or struct), a collection of fields . Product type (also called a tuple), a record in which the fields are not named
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 } .
A rearrangement of the entries of a banded matrix which requires less space. Sparse matrix: A matrix with relatively few non-zero elements. Sparse matrix algorithms can tackle huge sparse matrices that are utterly impractical for dense matrix algorithms. Symmetric matrix: A square matrix which is equal to its transpose, A = A T (a i,j = a j,i ...
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Matrix representation is a method used by a computer language to store column-vector matrices of more than one dimension in memory. Fortran and C use different schemes for their native arrays. Fortran uses "Column Major" ( AoS ), in which all the elements for a given column are stored contiguously in memory.
A band matrix with k 1 = k 2 = 0 is a diagonal matrix, with bandwidth 0. A band matrix with k 1 = k 2 = 1 is a tridiagonal matrix, with bandwidth 1. For k 1 = k 2 = 2 one has a pentadiagonal matrix and so on. Triangular matrices. For k 1 = 0, k 2 = n−1, one obtains the definition of an upper triangular matrix
The degree matrix indicates the degree of vertices. The Laplacian matrix is a modified form of the adjacency matrix that incorporates information about the degrees of the vertices, and is useful in some calculations such as Kirchhoff's theorem on the number of spanning trees of a graph.