Divide-and-conquer eigenvalue algorithms are a class of eigenvalue algorithms for Hermitian or real symmetric matrices that have recently (circa 1990s) become competitive in terms of stability and efficiency with more traditional algorithms such as the QR algorithm. The basic concept behind these algorithms is the 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 recursively, and the eigenvalues of the original problem are computed from the results of these smaller problems.
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| - Algoritmo eigenvalue divide y vencerás (es)
- Divide-and-conquer eigenvalue algorithm (en)
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| - Divide-and-conquer eigenvalue algorithms are a class of eigenvalue algorithms for Hermitian or real symmetric matrices that have recently (circa 1990s) become competitive in terms of stability and efficiency with more traditional algorithms such as the QR algorithm. The basic concept behind these algorithms is the 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 recursively, and the eigenvalues of the original problem are computed from the results of these smaller problems. (en)
- Los algoritmos Divide y Vencerás eigenvalue son una clase de algoritmos eigenvalue para hermitanos o matrices reales simétricas que recientemente (cerca de 1990) se han hecho competitivos en plazo de estabilidad y eficiencia con los algoritmos más tradicionales como algoritmos QR. El concepto básico detrás de estos algoritmos es divide y vencerás llevado a las ciencias informáticas.Un problema eigenvalue se divide en dos problemas de aproximadamente la mitad del problema general; cada uno de estos problemas es resuelto recursivamente y los eigenvalue del problema original son computados a partir de los resultados de los problemas más pequeños. (es)
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| - Divide-and-conquer eigenvalue algorithms are a class of eigenvalue algorithms for Hermitian or real symmetric matrices that have recently (circa 1990s) become competitive in terms of stability and efficiency with more traditional algorithms such as the QR algorithm. The basic concept behind these algorithms is the 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 recursively, and the eigenvalues of the original problem are computed from the results of these smaller problems. Here we present the simplest version of a divide-and-conquer algorithm, similar to the one originally proposed by Cuppen in 1981. Many details that lie outside the scope of this article will be omitted; however, without considering these details, the algorithm is not fully stable. (en)
- Los algoritmos Divide y Vencerás eigenvalue son una clase de algoritmos eigenvalue para hermitanos o matrices reales simétricas que recientemente (cerca de 1990) se han hecho competitivos en plazo de estabilidad y eficiencia con los algoritmos más tradicionales como algoritmos QR. El concepto básico detrás de estos algoritmos es divide y vencerás llevado a las ciencias informáticas.Un problema eigenvalue se divide en dos problemas de aproximadamente la mitad del problema general; cada uno de estos problemas es resuelto recursivamente y los eigenvalue del problema original son computados a partir de los resultados de los problemas más pequeños. Aquí presentamos la versión más sencilla de un algoritmo de dividir y vencerás, similar al originalmente propuesto por Cuppen en 1981. Muchos detalles que quedan fuera del alcance de este artículo serán omitidos; aun así, sin considerar estos detalles, el algoritmo no es plenamente estable. (es)
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