Sparse matrix: Difference between revisions

Revision as of 01:38, 27 February 2024

Revision as of 01:40, 27 February 2024

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* The arrays {{math|V}} and {{math|COL_INDEX}} are of length {{math|NNZ}}, and contain the non-zero values and the column indices of those values respectively

* {{math|COL_INDEX}} contains the column in which the corresponding entry {{math|V}} is located.

* The array {{math|ROW_INDEX}} is of length {{math|''m'' + ''1''}} and encodes the index in {{math|V}} and {{math|COL_INDEX}} where the given row starts. This is equivalent to {{math|ROW_INDEX[j]}} encoding the total number of nonzeros above row {{math|j}}. The last element is {{math|NNZ}} , i.e., the fictitious index in {{Math|V}} immediately after the last valid index {{math|NNZ - 1}}.<ref name=":0">{{cite book |last1=Saad |first1=Yousef |title=Iterative methods for sparse linear systems |date=2003 |publisher=SIAM}}</ref>

For example, the matrix

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* {{Cite web |title=Sparse Matrix Multiplication Package|first1= Randolph E.|last1= Bank|first2= Craig C.|last2= Douglas |url=http://www.mgnet.org/~douglas/Preprints/pub0034.pdf}}

* {{Cite book |last=Pissanetzky|first= Sergio|year= 1984|title=Sparse Matrix Technology|url=https://archive.org/details/sparsematrixtech0000piss|url-access=registration|publisher= Academic Press|isbn= 9780125575805}}

*{{cite journal|doi=10.1007/BF02521587|title=Reducing the profile of sparse symmetric matrices|year=1976|last1=Snay|first1=Richard A.|journal=[[Bulletin Géodésique]]|volume=50|issue=4|pages=341–352|bibcode=1976BGeod..50..341S|hdl=2027/uc1.31210024848523|s2cid=123079384|hdl-access=free}} Also NOAA Technical Memorandum NOS NGS-4, National Geodetic Survey, Rockville, MD.<ref>{{cite namebook |last1=":0"Saad |first1=Yousef |title=Iterative methods for sparse linear systems |date=2003 |publisher=SIAM}}</ref>

* [https://link.springer.com/book/10.1007/978-3-031-25820-6 Jennifer Scott and Miroslav Tuma: "Algorithms for Sparse Linear Systems", Birkhauser, (2023), DOI: https://doi.org/10.1007/978-3-031-25820-6 (Open Access Book)]