License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
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DOI: 10.4230/DagSemProc.06271.13
URN: urn:nbn:de:0030-drops-7806
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Watt, Stephen M.

Pivot-Free Block Matrix Inversion

06271.WattStephen.Paper.780.pdf (0.2 MB)


We present a pivot-free deterministic algorithm for the inversion of block matrices. The method is based on the Moore-Penrose inverse and is applicable over certain general classes of rings. This improves on previous methods that required at least one invertible on-diagonal block, and that otherwise required row- or column-based pivoting, disrupting the block structure. Our method is applicable to any invertible matrix and does not require any particular blocks to invertible. This is achieved at the cost of two additional specialized matrix multiplications and, in some cases, requires the inversion to be performed in an extended ring.

BibTeX - Entry

  author =	{Watt, Stephen M.},
  title =	{{Pivot-Free Block Matrix Inversion}},
  booktitle =	{Challenges in Symbolic Computation Software},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6271},
  editor =	{Wolfram Decker and Mike Dewar and Erich Kaltofen and Stephen Watt},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-7806},
  doi =		{10.4230/DagSemProc.06271.13},
  annote =	{Keywords: Linear algebra, block matrices, matrix inverse}

Keywords: Linear algebra, block matrices, matrix inverse
Collection: 06271 - Challenges in Symbolic Computation Software
Issue Date: 2006
Date of publication: 02.11.2006

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