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Weighted Minimization Problems for Quaternion Matrices

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Abstract

We introduce three kinds of new weighted quaternion-matrix minimization problems in order to extend some well-known constrained approximation problems. The main result is the claim that these new minimization problems have unique solutions which are expressed in terms of expressions involving weighted core-EP inverse and its dual for adequate quaternion matrices. Also, determinantal expressions of solutions for considered minimization problems are given. Obtained theoretical results are justified by a numerical example.

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Change history

  • 17 June 2021

    The original online version of this article was revised to update some of the superscripts which in red color in XML.

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Authors and Affiliations

  1. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine 3-b, Naukova Str., L’viv, 79060, Ukraine

    Ivan I. Kyrchei

  2. Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, Niš, 18000, Serbia

    Dijana Mosić & Predrag S. Stanimirović

Authors
  1. Ivan I. Kyrchei
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  2. Dijana Mosić
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  3. Predrag S. Stanimirović
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Correspondence to Dijana Mosić.

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Communicated by G. Stacey Staples

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Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Dijana Mosić accepts support from the Ministry of Education, Science and Technological Development, Republic of Serbia under grant 174007/451-03-9/2021-14/200124.

Predrag S. Stanimirović accepts support from the Ministry of Education and Science, Republic of Serbia under grant 174013/451-03-9/2021-14/200124.

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Kyrchei, I.I., Mosić, D. & Stanimirović, P.S. Weighted Minimization Problems for Quaternion Matrices. Adv. Appl. Clifford Algebras 31, 48 (2021). https://doi.org/10.1007/s00006-021-01153-4

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