Divide-and-conquer eigenvalue algorithm

<p>Divide-and-conquer eigenvalue algorithms are a class of <a href="/facts/Eigenvalue_algorithm/AYecadB0">eigenvalue algorithms</a> for <a href="/facts/Hermitian_matrix/qArPblYo">Hermitian</a> or <a href="/facts/Real_number/R02gw5Pb">real</a> <a href="/facts/Symmetric_matrix/08CGwjNl">symmetric matrices</a> that have recently (circa 1990s) become competitive in terms of <a href="/facts/Numerical_stability/jRDdo8zV">stability</a> and <a href="/facts/Computational_complexity_theory/etHuVF3U">efficiency</a> with more traditional algorithms such as the <a href="/facts/QR_algorithm/7LfgtT40">QR algorithm</a>.  The basic concept behind these algorithms is the <a href="/facts/Divide_and_conquer_algorithm/pC1X7Ws7">divide-and-conquer</a> approach from <a href="/facts/Computer_science/lN3pEyPz">computer science</a>.  An <a href="/facts/Eigenvalue/8TjEoT8u">eigenvalue</a> problem is divided into two problems of roughly half the size, each of these are solved <a href="/facts/Recursion/CxSKxJoW">recursively</a>, and the eigenvalues of the original problem are computed from the results of these smaller problems.
</p><p>This article covers the basic idea of the algorithm as originally proposed by Cuppen in 1981, which is not numerically stable without additional refinements.
</p>

Divide-and-conquer eigenvalue algorithm open-in-new

Divide-and-conquer eigenvalue algorithm