Definition: A matrix that has relatively few non-zero (or "interesting") entries. It may be represented in much less than n × m space.
Aggregate child (... is a part of or used in me.)
list, orthogonal lists, array, or point access method.
See also ragged matrix, huge sparse array.
Note: A n × m matrix with k non-zero entries is sparse if k << n × m. It may be faster to represent the matrix compactly as a list of the non-zero entries in coordinate format (the value and its row/column position), as a list or array of lists of entries (one list for each row), two orthogonal lists (one list for each column and one list for each row), or by a point access method.
Yousef Saad's Iterative methods for sparse linear systems (PDF), chapters 1-3 of a textbook covering linear algebra and types of matrices. Sparse matrix implementations, including the coordinate format, begin on page 85 (PDF page 97). Other formats and information on a newer edition.
If you have suggestions, corrections, or comments, please get in touch with Paul E. Black.
Entry modified 18 December 2009.
HTML page formatted Tue Dec 6 16:16:32 2011.
Cite this as:
Paul E. Black, "sparse matrix", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 18 December 2009. (accessed TODAY) Available from: http://www.nist.gov/dads/HTML/sparsematrix.html