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Everything about Eigenvalue algorithm
Numerical methods for matrix eigenvalue calculation
In numerical analysis, one of the most important problems is designing efficient and stable algorithms for finding the eigenvalues of a matrix. These eigenvalue algorithms may also find eigenvectors. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Eigenvalue algorithmA 5-minute orientation
- Skim a recent paper: An efficient algorithm for the eigenvalue problem of a Hermitian quaternion matrix in quantum chemistryInfluential work since 2022
- Pick up a classic book: Quotient-difference type generalizations of the power method and their analysisThe most-reprinted book on the subject
- Read the landmark paper: An Algorithm for Generalized Matrix Eigenvalue ProblemsCited 876 times
- Go sideways: Eigendecomposition of a matrixA closely related topic
- Go sideways: Eigenvalues and eigenvectorsA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
An Algorithm for Generalized Matrix Eigenvalue Problems
Density-matrix-based algorithm for solving eigenvalue problems
A Fully Parallel Algorithm for the Symmetric Eigenvalue Problem
A simultaneous iteration algorithm for symmetric eigenvalue problems
An efficient Jacobi-like algorithm for parallel eigenvalue computation
A nonsmooth algorithm for cone-constrained eigenvalue problems
A linear eigenvalue algorithm for the nonlinear eigenvalue problem
An Algorithm for the Ill-Conditioned Generalized Eigenvalue Problem
🆕 Influential since 2022
An efficient algorithm for the eigenvalue problem of a Hermitian quaternion matrix in quantum chemistry
Rapid Prediction of Compressor Rotating Stall Inception Using Arnoldi Eigenvalue Algorithm
Extended Wittrick–Williams algorithm for eigenvalue solution of stochastic dynamic stiffness method
Scalable Analytic Eigenvalue Extraction Algorithm
Variational quantum algorithm for generalized eigenvalue problems and its application to the finite-element method
📚 Books worth reading
- 📕Quotient-difference type generalizations of the power method and their analysisAvram Sidi · 1989
- 📕Modern algorithms for large sparse eigenvalue problemsArnd Meyer · 1987
Symplectic Methods for the Symplectic EigenproblemHeike Fassbender · 2007
The Lanczos methodLouis Komzsik · 1987- 📕A parallel solution for the symmetric eigenproblemGaylen A. Thurston · 1987
- 📕A robust multilevel simultaneous eigenvalue solverSorin Costiner · 1993
- 📕An O(logN) parallel algorithm for computing the Eigenvalues of a symmetric tridiagonal matrixPaul N. Swarztrauber · 1989
A parallel algorithm for symmetric tridiagonal eigenvalue problemsHui-ming Huang · 1974
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Eigendecomposition of a matrix In linear algebra, eigendecomposition (also known as eigenvalue decomposition or EVD) is a factorization of a matrix A into a canonical form given by A=QDQ−𝟣…
- Eigenvalues and eigenvectors In linear algebra, an eigenvector (/ˈaɪɡən-/ EYE-gən-) or characteristic vector is a (nonzero) vector that has its direction unchanged (or reversed) by…
- Characteristic polynomial In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues…
- Generalized eigenvector In linear algebra, a generalized eigenvector of an n×n matrix A is a vector which satisfies certain criteria which are more relaxed than those for an (ordinary)…
- Jordan normal form [⌜λ11⌝λ11⌞λ1⌟⌜λ21⌝⌞λ2⌟[λ3]⋱⌜λn1⌝⌞λn⌟] Example of a matrix in Jordan normal form. All matrix entries not shown are zero. The outlined squares are known…
- Frobenius covariant In matrix theory, the Frobenius covariants of a square matrix A are special polynomials of it, namely projection matrices Fi(A) associated with the eigenvalues…
- Diagonalizable matrix In linear algebra, a square matrix A is called diagonalizable or non-defective if it is similar to a diagonal matrix. That is, if there exists an invertible…
- Normal matrix In mathematics, a complex square matrix A is normal if it commutes with its conjugate transpose A*: A normal⟺A∗A=AA∗. The concept of normal matrices can…