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.

中文翻译：

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三对角矩阵族的特征对：三年后

这篇综述论文总结了基于 Losonczi 近 30 年前开创性工作的三对角矩阵族本征对公式的最近更重要的应用，这些工​​作似乎不仅在很大程度上被忽略了，而且还被重铸或重新定义。从那以后，各种作者以不同的形式发现。在介绍这些应用程序的过程中，我们还接触了早期更具体的应用程序，在这些应用程序中，Losonczi 的工作可以被应用以更快地产生结果。物理学和工程学中的许多最近的应用都引用了不那么普遍的工作，十多年后 Losonczi 也这样做了。