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On the Relation between the AINV and the FAPINV Algorithms

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  • Davod Khojasteh Salkuyeh
  • Hadi Roohani

Abstract

The approximate inverse (AINV) and the factored approximate inverse (FAPINV) are two known algorithms in the field of preconditioning of linear systems of equations. Both of these algorithms compute a sparse approximate inverse of matrix ð ´ in the factored form and are based on computing two sets of vectors which are ð ´ -biconjugate. The AINV algorithm computes the inverse factors ð ‘Š and ð ‘ of a matrix independently of each other, as opposed to the AINV algorithm, where the computations of the inverse factors are done independently. In this paper, we show that, without any dropping, removing the dependence of the computations of the inverse factors in the FAPINV algorithm results in the AINV algorithm.

Suggested Citation

  • Davod Khojasteh Salkuyeh & Hadi Roohani, 2009. "On the Relation between the AINV and the FAPINV Algorithms," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2009, pages 1-6, November.
    • Handle: RePEc:hin:jijmms:179481
    DOI: 10.1155/2009/179481
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    Cited by:

    1. F. Soleymani, 2012. "A Rapid Numerical Algorithm to Compute Matrix Inversion," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-11, September.

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