Comments (2)
yixuan
commented on September 15, 2024
This is related to what I call a sequential PCA: http://ieeexplore.ieee.org/abstract/document/8258403/.
The idea is actually very simple: for a matrix A, if you have computed the largest k eigenvalues Dk and eigenvectors Gk, then the (k+1)-th eigenvalue is the largest eigenvalue of A - Gk * Dk * Gk'. In this way you can compute the eigenvalues sequentially until your termination condition is met.
The tricky part is how to properly define the matrix operator, and how to "warm start" from previous calculations.
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eduardotsimoes
commented on September 15, 2024
Hello, any news on this front? It would be nice to be able to reuse the Ritz base from the previous iteration.
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Related Issues (20)
- Eigen decomposition failing on a real symmetric (Laplacian) matrix HOT 3
- Spectra doesn't accept non-literal data types anymore HOT 2
- SymGEigsSolver does not produce an orthonormal system of EigenVectors HOT 4
- Spectra as a practical ARPACK replacement HOT 1
- Support eigenvalue condition number
- difficulty in linking spectra header to visual studio 2022 preventing Build HOT 1
- compilation issues with the 'Spectra::SymEigsSolver' constructor. The error message is... HOT 2
- Silence error while solving the eigenvalues of a 2-by-2 matrix. HOT 5
- Issue with low-rank matrices HOT 5
- Limit of the matrix size for sparse Eigendecomposition; memory or CPU? HOT 2
- expanded application of Spectra to complex-valued matrices: problem of inequality signs in Arnoldi.h HOT 3
- ArnoldiOp.h, negative vnorm HOT 2
- Eigen value and generalized eigen value of a Super Big Size Real Matrix(160000*160000) , Help!
- GenEigsComplexShiftSolver compilation error; std::complex is being instantiated with std::complex<double> HOT 3
- Puzzling performance with Spectra when solving a general eigen for large sparse matrix (real symmetric both L and M)
- How does spectra compare to Matlab eigs
- Support for complex-valued matrices
- build failed on epel-9 ppc64le, `/usr/include/eigen3/Eigen/src/Core/arch/AltiVec/MatrixProductCommon.h:215:28: error: inlining failed in call to 'always_inline' 'Eigen::internal::ploadRhs<float, float __vector(4)>(float const*)float __vector(4)': target specific option mismatch`
- Generalized Eigenvalue - Support for positive semi-definite but singular matrices
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