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A Note on the Sensitivity of Generic Approximate Sparse Pseudoinverse Matrix for Solving Linear Least Squares Problems

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Advances in Parallel & Distributed Processing, and Applications

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Abstract

During the last decades, research efforts have been focused on the derivation of effective explicit preconditioned iterative methods. In this manuscript, we review the Explicit Preconditioned Conjugate Gradient Least Squares method, based on generic sparse approximate pseudoinverses, in conjunction with approximate pseudoinverse sparsity patterns, based on the modified row-threshold incomplete QR factorization techniques. Additionally, modified Moore-Penrose conditions are presented, and theoretical estimates for the sensitivity of the generic approximate sparse pseudoinverses are derived. Finally, numerical results concerning the generic approximate sparse pseudoinverses by solving characteristic model problems are given. The theoretical estimates were in qualitative agreement with the numerical results.

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Acknowledgements

The authors acknowledge the Greek Research and Technology Network (GRNET) for the provision of the National HPC facility ARIS under project PR004033-ScaleSciCompII and PR006053-ScaleSciCompIII.

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Authors and Affiliations

  1. Department of Informatics and Telematics, Harokopio University of Athens, Athens, Greece

    A. D. Lipitakis & D. Anagnostopoulos

  2. Department of Electrical and Computer Engineering, School of Engineering, Democritus University of Thrace, University Campus, Xanthi, Greece

    G. A. Gravvanis

  3. Western Gateway Building, University College Cork, Cork, Ireland

    C. K. Filelis-Papadopoulos

Authors
  1. A. D. Lipitakis
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  2. G. A. Gravvanis
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  3. C. K. Filelis-Papadopoulos
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  4. D. Anagnostopoulos
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Corresponding author

Correspondence to A. D. Lipitakis .

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Georgia, Athens, GA, USA

    Hamid R. Arabnia

  2. School of Computing and Data Sciences, Wentworth Institute of Technology, Boston, MA, USA

    Leonidas Deligiannidis

  3. Center for Cyberspace Research (CCR), Air Force Institute of Technology, Wright-Patterson AFB, OH, USA

    Michael R. Grimaila

  4. Electrical and Computer Engineering, Air Force Institute of Technology, Wright-Patterson AFB, OH, USA

    Douglas D. Hodson

  5. Information and Computer Sciences, Nara Women’s University, Nara, Japan

    Kazuki Joe

  6. School of Computing, Tokyo Institute of Technology, Meguro City, Japan

    Masakazu Sekijima

  7. Facultad de Informática - CIC PBA, Universidad Nacional de La Plata, La Plata, Argentina

    Fernando G. Tinetti

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Lipitakis, A.D., Gravvanis, G.A., Filelis-Papadopoulos, C.K., Anagnostopoulos, D. (2021). A Note on the Sensitivity of Generic Approximate Sparse Pseudoinverse Matrix for Solving Linear Least Squares Problems. In: Arabnia, H.R., et al. Advances in Parallel & Distributed Processing, and Applications. Transactions on Computational Science and Computational Intelligence. Springer, Cham. https://doi.org/10.1007/978-3-030-69984-0_21

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  • DOI: https://doi.org/10.1007/978-3-030-69984-0_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-69983-3

  • Online ISBN: 978-3-030-69984-0

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