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Algebraic Techniques for Least Squares Problems in Elliptic Complex Matrix Theory and Their Applications
  • Hidayet Kösal,
  • Müge Pekyaman
Hidayet Kösal
Sakarya University
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Müge Pekyaman
Sakarya University
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Abstract

In this study, we introduce concepts of norms of elliptic complex matrices and derive the least squares solution, the pure imaginary least squares solution, and the pure real least squares solution with the least norm for the elliptic complex matrix equation AX=B by using the real representation of elliptic complex matrices. To prove the authenticity of our results and to distinguish them from existing ones, some illustrative examples are also given. Elliptic numbers are generalized form of complex and so real numbers. Thus, the obtained results extend, generalize and complement some known least squares solutions results from the literature.

Peer review status:ACCEPTED

08 Dec 2020Submitted to Mathematical Methods in the Applied Sciences
09 Dec 2020Submission Checks Completed
09 Dec 2020Assigned to Editor
14 Dec 2020Reviewer(s) Assigned
12 Feb 2021Review(s) Completed, Editorial Evaluation Pending
12 Feb 2021Editorial Decision: Revise Minor
05 Mar 20211st Revision Received
05 Mar 2021Assigned to Editor
05 Mar 2021Submission Checks Completed
09 Mar 2021Reviewer(s) Assigned
24 Apr 2021Review(s) Completed, Editorial Evaluation Pending
05 May 2021Editorial Decision: Revise Minor
14 May 20212nd Revision Received
14 May 2021Submission Checks Completed
14 May 2021Assigned to Editor
17 May 2021Reviewer(s) Assigned
26 May 2021Review(s) Completed, Editorial Evaluation Pending
05 Jun 2021Editorial Decision: Accept