Pivot-Free Block Matrix Inversion

@article{Watt2006PivotFreeBM,
  title={Pivot-Free Block Matrix Inversion},
  author={Stephen M. Watt},
  journal={2006 Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing},
  year={2006},
  pages={151-155}
}
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… CONTINUE READING

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