qabot-zh / rank1-svd-update

Updating Singular Value Decomposition (SVD) for rank-1 perturbed matrix.

Rank-1 Singular Value Decomposition Updating Algorithm

This MATLAB library implements algorithm for updating Singular Value Decomposition (SVD) for rank-1 perturbed matrix using Fast Multipole Method (FMM) in time, where is the precision of computation. Detailed explaination of the algorithm can be found in this paper.

Running the tests

Run randomTestData.m to define and generate random 1) Base matrix and 2) Rank-one update to the base matrix. randomTestData.m passes the generated base matrix to the function testSVDUFMM.m that computes updated singular values and vectors for the updated base matrix.

Citation

If you use this package for your work, please cite the corresponding paper as:

Gandhi, Ratnik, and Amoli Rajgor. "Updating Singular Value Decomposition for Rank One Matrix Perturbation." arXiv preprint arXiv:1707.08369 (2017)

or as BibTeX format:

@article{DBLP:journals/corr/GandhiR17,
  author    = {Ratnik Gandhi and
               Amoli Rajgor},
  title     = {Updating Singular Value Decomposition for Rank One Matrix Perturbation},
  journal   = {CoRR},
  volume    = {abs/1707.08369},
  year      = {2017},
  url       = {http://arxiv.org/abs/1707.08369},
  archivePrefix = {arXiv},
  eprint    = {1707.08369},
  timestamp = {Sat, 05 Aug 2017 14:55:59 +0200},
  biburl    = {https://dblp.org/rec/bib/journals/corr/GandhiR17},
  bibsource = {dblp computer science bibliography, https://dblp.org}