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Tagged with krylov-method eigensystem
4 questions
7
votes
0
answers
371
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Implementation of Lanczos method that returns tridiagonal matrix
The Lanczos method can be used to obtain extremal eigenpairs of sparse symmetric or hermitian matrices. I know there are several implementations of the Lanczos method (as well as Arnoldi, Davidson, ...
- 171
2
votes
0
answers
228
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Generalized eigenvalue with null space
Define $S\in\mathbb{R}^{n\times n}$ as
$$S:=H+Q^\top V^{-1} Q.$$
$H,V$ are positive semidefinite. Here, $H$, $Q$, and $V$ are large, dense matrices but they are structured: I can write code for ...
- 1,433
4
votes
1
answer
351
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Appropriate iterative linear solver for an eigenvalue problem
I'm trying to solve a generalized eigenvalue problem
$$Ax = \lambda Bx, \quad A = A^\top > 0,\; B = B^\top > 0$$
with $\lambda \approx \sigma$ using Rayleigh Quotient Iteration (RQI) (RQI is ...
- 165
7
votes
1
answer
188
views
Identifying the name/provenance of a technique to find the nullspace vectors of a matrix by random sampling and the conjugate residual method
I have got a large sparse matrix $A \in \mathbb R^{n \times n}$ and I want to find non-trivial elements in the kernel/nullspace of this matrix. How can this be done? I would like to learn more about a ...
- 3,720