Abstract
The numerical rank determination frequently occurs in matrix computation when the conventional exact rank of a hidden matrix is desired to be recovered. This paper presents a Matlab package RankRev that implements two efficient algorithms for computing the numerical rank and numerical subspaces of a matrix along with updating/downdating capabilities for making adjustment to the results when a row or column is inserted/deleted. The package and the underlying algorithms are accurate, reliable, and much more efficient than the singular value decomposition when the matrix is of low rank or low nullity.
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Acknowledgements
The authors are grateful to the anonymous referees for their comments and suggestions.
Research of Tsung-Lin Lee was supported in part by the Taiwan MOST Grant 105-2115-M-110-005. Research of Tien-Yien Li was supported in part by NSF under Grant DMS 11-15587. Research of Zhonggang Zeng was supported in part by NSF under Grant DMS 1620337.
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Lee, TL., Li, TY. & Zeng, Z. RankRev: aMatlab package for computing the numerical rank and updating/downdating. Numer Algor 77, 559–576 (2018). https://doi.org/10.1007/s11075-017-0328-7
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DOI: https://doi.org/10.1007/s11075-017-0328-7