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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 ...
This is equivalent, by transposing the incidence matrix, to the hitting set problem. [2] [3]: SP5, SP8 Set packing [2] [3]: SP3 Set splitting problem [3]: SP4 Scheduling to minimize weighted completion time; Block Sorting [44] (Sorting by Block Moves) Sparse approximation; Variations of the Steiner tree problem. Specifically, with the ...
This is a list of well-known data structures. For a wider list of terms, see list of terms relating to algorithms and data structures. For a comparison of running times for a subset of this list see comparison of data structures.
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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Sparse approximation ideas and algorithms have been extensively used in signal processing, image processing, machine learning, medical imaging, array processing, data mining, and more. In most of these applications, the unknown signal of interest is modeled as a sparse combination of a few atoms from a given dictionary, and this is used as the ...
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.
They can, for example, be used to represent sparse graphs without incurring the space overhead from storing the many zero entries in the adjacency matrix of the sparse graph. In the following section the adjacency matrix is assumed to be represented by an array data structure so that zero and non-zero entries are all directly represented in ...