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Tagged with iterative-method eigensystem
8
questions
4
votes
0answers
29 views
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, ...
0
votes
0answers
27 views
A preconditioner for self-consistent iteration
I tried to derive a preconditioner for self-consistent iteration similar
to section IX in arXiv:0804.2583.
For simplicity, consider here only
one orbital (one or two electrons) systems.
Suppose that ...
2
votes
0answers
131 views
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 ...
5
votes
1answer
2k views
Quality of eigenvalue approximation in Lanczos method
I try to familiarize myself with iterative eigenvalue solvers such as Lanczos. So I tried rewrite it to python directly according to wiki. But it doesn't seem to work.
The problem:
it approximates ...
11
votes
1answer
707 views
Smallest eigenvalue without inverse
Suppose $A\in\mathbb{R}^{n\times n}$ is a symmetric, positive definite matrix. $A$ is big enough that it's expensive to solve $Ax=b$ directly.
Is there an iterative algorithm for finding the ...
4
votes
1answer
316 views
Finding interior eigenvalues using Davidson algorithm
Is it possible to find interior eigenvalues closer to some lambda using Davidson method? I was searching online but found that most people use Jacobi-Davidson method for that.
6
votes
3answers
1k views
Eigenvectors with the Power Iteration
To compute the eigenvector corresponding to dominant eigenvalue of a symmetric matrix $A\in\mathbb{R}^{n\times n}$, one used Power Iteration, i.e., given some random initialization, $u_1\in\mathbb{R}^...
8
votes
1answer
3k views
What is a good stop criterion when using an iterative method to find eigenvalues?
I read this answer, and realized I have been using the difference between sucessive iterates to define a stop criterion for an iterative method of finding eigenvalues/vectors.
What are good stop ...
