Tagged Questions

0
votes
1answer
27 views

Two Lagrange multipliers with one equation

I have an equation as below, $$Rw = \lambda_1R_aw + \lambda_2R_bw $$ where, $R$, $R_a$, and $R_b$ are positive definite at least semi-positive definite and Hermitian matrix. $\lambda_1$ and ...
0
votes
1answer
22 views

Simultaneous eigenfunction problems

I'm familiar with solving eigenfunction problems using finite difference methods and eigenvalue solver like Eigensystem[] in Mathematica. But now I've come across a problem where I have two ...
4
votes
2answers
109 views

Math hack for solving system of equations

Is it a "standard" Math/Numerical-Analysis hack to add a relatively small number e.g. 1*10E-5 to the diagonal of a squared matrix to ensure LU Decomposition (or whichever decomposition algorithm is ...
2
votes
2answers
559 views

Power iteration smallest eigenvalue?

I need to write a program which computes the largest and the smallest (in terms of absolute value) eigenvalues using both Power Iteration and Inverse Iteration. I can find them using the Inverse ...
0
votes
1answer
145 views

Sturm-Liouville problem: eigenvalues

I have a Sturm-Liouville problem $$ y'' + \lambda^2 y = 0, \\ y'(0) + \alpha_1 y(0) = 0, \\ y'(L) + \alpha_2 y(L) = 0, $$ where $\alpha_1 \alpha_2 \neq 0$. I found that eigenvalues are ...
1
vote
1answer
59 views

Numerical Computation of Eigenvalues

I am trying to find the first few eigenvalues of an operator defined by the following PDE: $$ \begin{cases} -\Delta u +(1-\varphi)u=\lambda u, & \text{ on }\Omega = [0,1]^2 \\ u=0 & \text{ ...
2
votes
1answer
218 views

How to determine the N-smallest eigenvalues of a symmetric matrix using the Power Method?

I was assigned to make a program that finds the largest, the N-largest, the smallest and the N-smallest eigenvalues of a symmetric matrix, using the Power Method. So far, I've been able to succesfully ...
4
votes
2answers
177 views

Is there a version of the Gershgorin circle theorem that is suitable for nearly triangular matricies?

The Gershgorin circle theorem, http://en.wikipedia.org/wiki/Gershgorin_circle_theorem, gives bounds on the eigenvalues of a square matrix, and works well for nearly diagonal matrices. For a ...
0
votes
3answers
281 views

program for eigenvalue calculation

I have a n x n matrix. I would like to (a) take successively higher powers of the matrix and then multiply by projection vectors until the resulting vectors differ by only a scalar factor. (b) ...
0
votes
3answers
300 views

Two linearly independent eigenvectors with eigenvalue zero

What is the only $2\times 2$ matrix that only has eigenvalue zero but does have two linearly independent eigenvectors? I know there is only one such matrix, but I'm not sure how to find it.
5
votes
1answer
548 views

Using the Arnoldi Iteration to find the k largest eigenvalues of a matrix

I'm trying to obtain a general understanding of this algorithm which determines the k-largest eigenvalues of a matrix $A\in \mathbb{R}^{n\times n}$. How I see it: power iteration: take random ...
-1
votes
2answers
514 views

Library for Jacobi eigenvalue algorithm [closed]

I am looking for a C or C++ or fortran library that implements the Jacobi eigenvalue algorithm: http://en.wikipedia.org/wiki/Jacobi_eigenvalue_algorithm do you know if it is available?
1
vote
0answers
412 views

Shifted Power Method

Using the shifted power method I find the eigenvalue (of the matrix A) farthest from a number $\mu$ and the corresponding eigenvector . In the method I follow the below steps: I first compute the ...
2
votes
3answers
284 views

What is a robust and reliable way/library for eigenvalues of 3x3 matrices?

I use Eigen to compute the eigenvalues of symmetric matrices. The problem is, that sometimes the matrices not nice at all numerically. Because of this, I get NaN among the eigenvalues. I have tested ...
3
votes
1answer
216 views

How do iterative methods applied to the companion matrix of a polynomial $p(\lambda)$ relate to $p$ itself?

A few days ago, I had a vague question in my mind about "matrix methods" for finding roots of a polynomial. Now I can ask at least a semi-precise question, thanks to the post How to calculate complex ...