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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 ...
Collaborative (joint) sparse coding: The original version of the problem is defined for a single signal . In the collaborative (joint) sparse coding model, a set of signals is available, each believed to emerge from (nearly) the same set of atoms from . In this case, the pursuit task aims to recover a set of sparse representations that best ...
In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal. If the graph is undirected (i.e. all of its edges are bidirectional), the adjacency matrix is symmetric. The relationship between a graph and the eigenvalues and eigenvectors of its adjacency matrix is studied in spectral graph theory.
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.
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 ...
A matrix which is equal to the negative of its transpose, A T = −A. Skyline matrix: 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 ...
Matrix representation; Morton order, another way of mapping multidimensional data to a one-dimensional index, useful in tree data structures; CSR format, a technique for storing sparse matrices in memory; Vectorization (mathematics), the equivalent of turning a matrix into the corresponding column-major vector
In numerical mathematics, hierarchical matrices (H-matrices) [1] [2] [3] are used as data-sparse approximations of non-sparse matrices. While a sparse matrix of dimension can be represented efficiently in () units of storage by storing only its non-zero entries, a non-sparse matrix would require () units of storage, and using this type of matrices for large problems would therefore be ...