Editing Divide-and-conquer eigenvalue algorithm (section)

{{Short description|Algorithm on Hermitian matrices}}
{{Multiple issues|
{{No footnotes|date=May 2024}}
{{More citations needed|date=May 2024}}
}}

'''Divide-and-conquer eigenvalue algorithms''' are a class of [[eigenvalue algorithm]]s for [[Hermitian matrix|Hermitian]] or [[real number|real]] [[Symmetric matrix|symmetric matrices]] that have recently (circa 1990s) become competitive in terms of [[Numerical stability|stability]] and [[Computational complexity theory|efficiency]] with more traditional algorithms such as the [[QR algorithm]].  The basic concept behind these algorithms is the [[Divide and conquer algorithm|divide-and-conquer]] approach from [[computer science]].  An [[eigenvalue]] problem is divided into two problems of roughly half the size, each of these are solved [[Recursion|recursively]], and the eigenvalues of the original problem are computed from the results of these smaller problems.

This article covers the basic idea of the algorithm as originally proposed by Cuppen in 1981, which is not numerically stable without additional refinements.