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Everything about Divide-and-conquer eigenvalue algorithm
Algorithm on Hermitian matrices
Divide-and-conquer eigenvalue algorithms are a class of eigenvalue algorithms for Hermitian or real symmetric matrices that have recently 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. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Divide-and-conquer eigenvalue algorithmA 5-minute orientation
- Read the landmark paper: A Parallel Divide and Conquer Algorithm for the Symmetric Eigenvalue Problem on Distributed Memory ArchitecturesCited 64 times
- Go sideways: Lanczos algorithmA closely related topic
- Go sideways: Arrowhead matrixA closely related topic
📖 Definitions
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🗂️ The subject at a glance
🏆 Landmark papers (most cited)
A Parallel Divide and Conquer Algorithm for the Symmetric Eigenvalue Problem on Distributed Memory Architectures
Divide and conquer algorithms for the bandsymmetric eigenvalue problem
Practical improvement of the divide-and-conquer eigenvalue algorithms
Toward a High Performance Tile Divide and Conquer Algorithm for the Dense Symmetric Eigenvalue Problem
A Parallel Structured Divide-and-Conquer Algorithm for Symmetric Tridiagonal Eigenvalue Problems
New fast divide‐and‐conquer algorithms for the symmetric tridiagonal eigenvalue problem
A divide and conquer algorithm on the double dimensional inverse eigenvalue problem for Jacobi matrices
Towards a Divide and Conquer Algorithm for the Real Nonsymmetric Eigenvalue Problem
📚 Books worth reading
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🔗 Related topics
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