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Eigenpairs of a family of tridiagonal matrices: three decades later

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Abstract

This survey paper summarizes the more important recent applications of the eigenpairs formulas for a family of tridiagonal matrices based on Losonczi’s seminal work of almost thirty years ago, which not only seems to have been largely ignored, but has also been re-cast or re-discovered in alternative guises by various authors since. In the course of presenting these applications, we also make contact with earlier more specific applications where Losonczi’s work could have been applied to yield the results more quickly. Many of the recent applications in physics and engineering cite less general work, which followed Losonczi more than a decade later.

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Authors and Affiliations

  1. Kuwait College of Science and Technology, Doha District, Block 4, P.O. Box 27235, Safat, 13133, Kuwait

    C. M. Da Fonseca

  2. University of Primorska, FAMNIT, Glagoljsaška 8, 6000, Koper, Slovenia

    C. M. Da Fonseca

  3. Department of Mathematics and Statistics, University of Melbourne, Victoria, 3010, Australia

    V. Kowalenko

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  1. C. M. Da Fonseca
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Correspondence to C. M. Da Fonseca.

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Da Fonseca, C.M., Kowalenko, V. Eigenpairs of a family of tridiagonal matrices: three decades later. Acta Math. Hungar. 160, 376–389 (2020). https://doi.org/10.1007/s10474-019-00970-1

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  • DOI: https://doi.org/10.1007/s10474-019-00970-1

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