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47 views

Computing eigenvectors from the QR algorithm

I've seen a few other posts on this topic but none have full answers. I'm trying to implement some eigen-decomposition algorithms. I've managed to get the Explicit QR algorithm and the Implicit ...
3
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0answers
46 views

scipy.linalg.sparse.eigsh does not work for generalised eigenvalues

I asked this question over at StackOverflow and someone told me that I'd get a better answer here. So here's my problem: I'm working on a machine learning project which involves doing a Principal ...
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0answers
37 views

Reorder eigenvalues in QZ factorization in Python-Scipy /Matlab [closed]

Python and Scipy seem capable of replicating the QZ factorization of Matlab when the option "complex" is used in the command scipy.scipy.linalg.qz Yet, it seems that is still not possible to obtain ...
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1answer
227 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
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2answers
115 views

Known issues with eigenvalue numerics?

Are there any known issues (such as precision issues) with $\mathsf{MATLAB}$ eig and charpoly functions for large enough $\{-1,0,+1\}$ matrices? Even if I change $1$ or $2$ entries between matrices ...
3
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1answer
51 views

Calculating left eigenvector when I know the right eigenvector

I'm using power iteration to find the dominant right eigenvector of some large-ish matrices ($1000\times 1000$ to $10000\times 10000$ or so, maybe I'll need to go bigger later) with non-negative ...
3
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0answers
94 views

Eigenvalue-style optimization with quadratic constraints

Suppose $A\in\mathbb{R}^{n\times n}$ is symmetric and positive definite and that we have several symmetric matrices $B_i\in\mathbb{R}^{n\times n}$ that are low-rank and indefinite. I need an ...
1
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1answer
61 views

solving a hyperbolic set of equations - upwind type method

I want to solve a set of hyperbolic equations (not the Euler equations) using an upwind type method. I am interested in using a first order upwind scheme and one that is not based on the method of ...
3
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2answers
140 views

what do zero real parts of eigenvalues mean? Any good references?

I am solving a 1D advection problem of the the form $$dQ/dt=[A]Q$$ where {Q} is the vector of unknowns and [A] is the matrix of coefficients of spatial discretisation. I have worked out the ...
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0answers
32 views

How to implement the eigendecomposition of a dense, non-hermitian matrix using cuSolver?

I am looking for a clear example on how to obtain the complete set of eigenvalues and eigenvectors of a matrix using cuSolver. I am also interested on the eigendecomposition of symmetric, tridiagonal ...
3
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2answers
190 views

Accuracy of numerical methods in finding eigenvalues

I have a problem with assesing the accuracy of my numerical calculation. I have a 2nd order ODE. It is an eigenvalue problem of the form: $$ y'' + ay' + \lambda^2y = 0, $$ and the boundary condiations ...
2
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0answers
105 views

what do positive real parts of eigenvalues mean?

I am solving a 1D advection problem of the the form $$d{Q}/dt = [A]{Q}$$ where {Q} is the vector of unknowns and [A] is the matrix of coefficients of spatial discretisation. I have worked out the ...
2
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1answer
92 views

Improving my QZ-Algorithm (Include Shifts)

I Need to to solve an generalized Eigenvalue Problem and to compare two Methods (QR and QZ) concerning their convergence rate and execution time. I started with the Basic QR-Algorithm, implemented in ...
3
votes
1answer
62 views

linear stability analysis using spectral radius

I am analysing the stability of a series of 1D linear equations of the form \begin{equation} \frac{d}{dt} x = A x \end{equation} discretised using upwind and central finite volume methods, etc, with ...
1
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0answers
33 views

non convex, non linear optimization involving matrix differential equation solution

I'm trying to develop an inferential procedure for a multivariate dependent Markov process. Basically, the procedure could be considered as a non linear regression, with a known dependence structure ...
5
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3answers
92 views

Does the Lanczos starting vector have to be random?

In all descriptions of the Lanczos vector, it's said that the starting vector is random. But let's say I'm only interested in the eigenvector associated with the lowest eigenvalue (as is the case ...
1
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1answer
76 views

Sparse generalized eigensolver using OpenCL

I would like to solve a generalized eigenproblem of real sparse symmetric matrices. Is there an efficient library which utilizes OpenCL in order to find a limited amount of the smallest eigenvalues in ...
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0answers
89 views

generalized eigenvalue problem, SLEPcEigenSolver no eigenvalues with negative reals

We are working on the model of a kinematic fluid dynamo in FEniCS. It tries to explore whether a magnetic field can be excited if a conducting fluid flows with a certain velocity field through some ...
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0answers
37 views

Eigenvalues from graph (modal)

I am a power engineer analyzing the dynamic response to system events. I am trying to re-create a modal analysis function from older software in python. In this context modal analysis is taking a ...
2
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2answers
124 views

How to correctly normalize modulus and phase of an eigenvector?

I am solving a linear stability problem using finite element discretization. Then, I have a generalised eigenvalue problem: $$ \lambda M x = J x.$$ I obtain complex eigenvalue and eigenvectors from ...
3
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2answers
59 views

Is it possible to use Eigtool for generalized problem pseudospectra?

I would like to use the Eigtool of professor Trefethen for pseudospectra but I have a generalized eigenvalue problem to solve: $$ \lambda M x = K x. $$ It seems that Eigtool takes only one matrix as ...
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2answers
161 views

How can I prove that two eigenvectors are orthogonal?

I obtained 6 eigenpairs of a matrix using eigs of Matlab. How can I demonstrate that these eigenvectors are orthogonal to each other? I am almost sure that I ...
0
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1answer
60 views

How does the animation work in eigenvalue problem of FEM

I have used free vibration analysis in FEM. After analysis, we can usually use animation to see the motion of each eigenmode (In Abaqus or Comsol, I would choose either half harmonic or full ...
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0answers
155 views

Arpack and Matlab give different values for eigenvalues

I am solving a generalized eigenvalues problem with inversed complex shift: $$(M-\sigma J)^{-1}J \boldsymbol{x} = \boldsymbol{x} \nu \enspace .$$ My matrices are obtained from a finite element ...
2
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1answer
151 views

Computational methods for finding the energy eigenvalues of the time-independent Schrodinger equation with arbitrary potential

I have seen in some papers that the energy levels in some arbitrary potential are specified. How can one find the energy levels in such arbitrary potentials. For example, $V(x)=\sin^2(x/2)$ with ...
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0answers
31 views

Minimum effort merging of two sets

I have the following problem. I have two sequences of elements $A = [a_1,a_2,\cdots,a_n]$ and $B = [b_1,b_2,\cdots,b_m]$. I can build a matrix $D[n \times m]$ where $d_{ij} = d(a_i,b_j)$ My greedy ...
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0answers
31 views

Locally evaluate nonlinear dynamic system's stability using eigenvalues

I'm working with Computational Neuroscience. I have a large Synaptic Matrix (x axis: presynaptic NeuronID, y axis: postsynaptic NeuronID) in a Modular network. This matrix is close to a random one and ...
0
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1answer
184 views

Armadillo eig_sym() for extracting eigenvalues. Is it parallel at all? [closed]

After wasting 3 days with scalapack, I gave up and moved to Armadillo, considering it uses lapack underneath its beatiful and easy interface. I would like to calculate the eigen values and eigen ...
4
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1answer
65 views

Correctly orthogonalizing and normalizing eigenvectors of a non-hermitian problem

I have some non-hermitian matrix $A$, that I have the left and right eigenvectors. (Calculated using SLEPc, by finding the eigenvectors of $A$ and $A^H$). I'm not sure how to orthogonalize them ...
6
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1answer
126 views

Compute eigenvectors of a matrix with known eigenvalue spectrum

If I have already accurately known the eigenvalue spectrum (i.e. all eigenvalues) of a matrix, is there any efficient numerical algorithm to compute all the eigenvectors corresponding to these ...
3
votes
1answer
92 views

Derivative of a generalized eigenvalue problem

I want to compute the derivative of a generalized eigenvalue $\lambda$ which is solution of $A u = \lambda Bu$ ($A,B,u,\lambda$ all depend on $t$; in my case $A,B$ are known explicitly, and the ...
5
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1answer
141 views

roots of polynomials with small coefficients

I would like to compute the roots of a polynomial with exponentially small coefficients. $$ \sum_{n=0}^N a_n \frac{z^n}{\sqrt{n!}} \tag{$\ast$}$$ where $a_n$ are Normal random variables with mean ...
0
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0answers
104 views

Estimating the second largest eigenvalue

I am currently dealing with the following problem. I am given a matrix $A$ of order $n \times n$ where $n \leq 20.$ The principal $(n-1) \times (n-1)$ matrix of $A$ is symmetric and contains only ...
0
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1answer
351 views

Order of eigenvalue problem using c++ Eigen library

I have the following 6x6 matrix (taken from Google Books p. 129): For background info: All the entries depend on the momentum $k$. Getting the eigenvalues of this matrix for each $k$ corresponds to ...
2
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1answer
82 views

find the exact solution ref The finite element method using matlab by Kwon and Bang [closed]

The results found are as under how do we find the exact solution ref The finite element method using matlab by Kwon and Bang.Page no 280-281 Example no 8.10.1.
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0answers
80 views

Compute eigenvalues with Arpack

I am using Arpack to compute the eigenvalues of the problem $\lambda Mx = Ax$ with reverse shift method with complex shift. $A$ and $M$ are real, $M$ is symmetric. Then, I use znaupd e zneupd. I use ...
2
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1answer
215 views

Laplacian discretization for parametric curves

I know how to compute the discrete Laplacian of a graph and of a mesh (the Laplace-Beltrami operator). Is there an analogous definition for the computation of the Laplacian of a parametric curve ? ...
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0answers
218 views

eigs routine in octave

I am using octave and observed a problem with the eigs-routine for non symmetric matrices. Using GNU octave version 3.8.1 the code below gives significant difference of eigenvalues although same ...
1
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1answer
77 views

Parallel Monte Carlo simulation using PETSc

I am trying to do Monte Carlo simulation for a large problem which requires eigensolution of a matrix for each sample. The matrix itself is quite large so much so that I want the eigensolution itself ...
0
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2answers
68 views

Computing eigenpairs of singular matrix with ZGEEV?

I've never run into a singular matrix before, so bear with me. I have a complex non-symmetric matrix (about 1000 x 1000) that I know has a couple zero eigenvalues. It isn't guaranteed to be ...
0
votes
1answer
84 views

Solve eigenvalue problem using finite differences without vectorization

I am interested in solving the problem $-A u = \lambda u$ on a finite differences grid on a square. In my case, the operator $A$ is of the type $-\Delta + \mu I$, where $\mu$ is there to impose some ...
1
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0answers
128 views

ARPACK gives different answers from Matlab and NAG

I'm playing with ARPACK. I looked into the examples they provide, zndrv4.f illustrating the usage of the routine znaupd, in the directory of ARPACK/EXAMPLES/COMPLEX/. I also came cross NAG Fortran ...
1
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1answer
50 views

LAPACK DGGEVX: BALANC option

I'm using DGGEVX routine from LAPACKE with BALANC option as shown below, but to my surprise changing BALANC option from 'N' to ...
0
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0answers
182 views

I am looking for a complex sparse matrix EigenVector solver for GPGPU; preferably CUDA

So far the closest I've found is ViennaCL, which has a Lanczos implementation for Eigenvalues. It is not clear that EigenVectors are produced by this library. Does anyone here know whether ViennaCL ...
3
votes
2answers
858 views

Eigenvectors: MATLAB vs LAPACK DGGEV or DGGEVX

If we call LAPACK DGGEV or DGGEVX routines for two badly-conditioned matrices in a C++ code, will we get the same eigen-values ...
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0answers
35 views

Eigenvalues and Timestep restriction Follow up

This is a follow-up question to the previous questions I had on eigenvalues. Please let me know if I should edit the previous question itself for asking this. If the eigenvalues of a matrix ...
3
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1answer
226 views

Eigenvalues and Timestep restriction

For an equation of the kind $u_t=Au$, time step is usually defined by ensuring that the eigenvalues are within the stability region of the time-stepping scheme employed. If the eigenvalues are on ...
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0answers
53 views

smallest eigenvalues for linear elasticity

I want to compute a few tens of the smallest eigenvalues of a linear system which is a discretization of a linear elasticity. In the presence of additional constraints like Dirichlet boundary ...
0
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1answer
106 views

Deflation for generalized eigenvalue problem

We know that principle component analysis (PCA) is a eigenvalue problem. Let $A$ be the covariance matrix of $X$, PCA aims to find the eigenvalue of $A$: $\max v'Av$, subject to $v'v=1$ Multiple ...
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0answers
77 views

Eigenvalue analysis of preconditioned partial differential operator

today, I encountered a confused problem by accident, but I have no ideas to deal with it fully. The question can be described as follows: for example, when we need to use FDM/FEM to discrete the ...