Questions tagged [eigenvalues]
Eigenvalues are a special set of scalars associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic roots, characteristic values (Hoffman and Kunze 1971), proper values, or latent roots (Marcus and Minc 1988, p. 144).
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How to properly use ARAPCK's dsaupd and dseupd?
In rust, I am trying to solve an eigendecomposition problem through ARPACK. I made the following subroutine for this purpose:
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What are some good medium matrices with known eigenvectors?
I am trying to test if an eigendecomposition I have is working properly. For this I would like some matrices that are 10x10 (ish) with trivial (or known) eigenvectors and eigenvalues so that I can ...
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Fastest way to calculate the eigenvector with the largest eigenvalue for a 3*3 positive-definite matrix [duplicate]
As stated in the title: I have a 3 by 3 positive-definite matrix $M$. What I need is the eigenvector corresponding to the largest eigenvalue, since I am calculating the solution to maximize the value ...
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Eigenvalue Problem with Pseudospectral Chebyshev Polynomials
I am solving a linear 4th Order Eigenvalue ODE (Euler-Bernoulli Beam):
$$
{\frac{d^{4}w}{dx^{4}}} = - \alpha {\frac{d^{2}w}{dx^{2}}}
$$
The method I used was to apply a truncated spectral expansion ($...
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What is fastest method for finding the minimum and maximum eigenvalues of a (possibly very large) symmetric matrix?
What is the best way to find the extreme eigenvalues - in order to find the spectral radius - of a general real dense symmetric matrix?
Looking at similar questions e.g.: What's the most efficient ...
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2x2 complex symmetric eigendecomposition - LAPACK subroutine CLAESY
Asking here because I searched the LAPACK user forums and found nothing.
I have a problem that requires the computation of the eigendecomposition $A=A^T=Q \Lambda Q^T$ for the 2x2 complex symmetric ...
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Optimized Lanczos method for finding eigenvalues of $A \otimes B$
Recently my supervisor told me about an efficient way to calculate eigenvalues and eigenvectors of matrix $A \otimes B$ with $a_{1} \times a_{2}$ as dimensions of $A$ and $b_{1} \times b_{2}$ is of $B$...
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Matrix Diagonalization and Computational Requirements
I have some questions about diagonalizing matrices. My interest lies in computing all eigenvalues of a given matrix. To avoid wasting time and improve my research efficiency, I want to understand the ...
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Parallel vs Serial computing using Python Qutip. Why is serial faster?
I am trying to learn parallel computing using qutip's parallel_map function. I've tried to write a basic and simple code to understand the differences between parallel and serial calculation of ...
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'eigs()' in Matlab gives inaccurate eigenvector when only several eigenvalues are calculated
I would like to report an issue which may be interesting in computational physics. Sometimes, to save time and memory, we use eigs() to calculate the first several ...
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Best transform of matrix to make it efficient for shift-then-invert?
I am using ARPACK to find the smallest eigenvalue of a matrix. I use the shift and invert method. That is, looking for the largest eigenvalue of
$$
(A-\sigma I)^{-1}.
$$
However, I do not know $\sigma$...
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Why for $A^T A$, it is faster to computer the eigenvalues of its inverse than itself?
I have written the following code in MATLAB. I also observe the same effect in Arnoldi iteration in ARPACK in C.
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Ways to speed up Lanczos algorithm when we have a very dense cluster of many eigenvalues?
Lanczos algorithm can be used to find the largest/smallest eigenvalues of matrices. I am trying to find a good library in C/C++/Rust for finding the smallest singular value (or eigenvalue). I have ...
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Eigenvalue problem and pseudoinverse of a product of sparse matrices
If I have some dense matrix that can be decomposed into a product of sparse matrices with known(but different) sparsity patterns. Can I somehow use this information to more efficiently compute its ...
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using scipy.sparse.linalg.eigsh for degenerate states in Bose Hubbard model
I am currently writing a code for the Bose-Hubbard model, and I am calculating the ground states and single-particle density matrix for different values of U and J. As U=0, one would see how the ...
