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Computation of outer inverses of tensors using the QR decomposition

Abstract

In this paper, we introduce new representations and characterizations of the outer inverse of tensors through QR decomposition. Derived representations are usable in generating corresponding representations of main tensor generalized inverses. Some results on reshape operation of a tensor are added to the existing theory. An effective algorithm for computing outer inverses of tensors is proposed and applied. The power of the proposed method is demonstrated by its application in 3D color image deblurring.

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Acknowledgements

Ratikanta Behera is grateful to the Mohapatra Family Foundation and the College of Graduate Studies, University of Central Florida, Orlando, for their financial support for this research.

Predrag Stanimirović gratefully acknowledges support from the Ministry of Education, Science and Technological Development, Republic of Serbia, Grant No. 174013.

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Correspondence to Predrag S. Stanimirović.

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Communicated by Jinyun Yuan.

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Sahoo, J.K., Behera, R., Stanimirović, P.S. et al. Computation of outer inverses of tensors using the QR decomposition. Comp. Appl. Math. 39, 199 (2020). https://doi.org/10.1007/s40314-020-01225-4

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  • DOI: https://doi.org/10.1007/s40314-020-01225-4

Keywords

  • Outer inverse
  • Generalized inverse
  • QR Decomposition
  • Image deblurring
  • Einstein product

Mathematics Subject Classifications

  • 15A09
  • 15A10
  • 15A69