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).
Questions tagged [eigenvalues]
298 questions
8
votes
2 answers
Solving a generalised eigenvalue problem
I have a generalized eigenvalue problem in the standard form
$\lambda \mathbf{B} \mathbf{x} = \mathbf{A} \mathbf{x} $,
resulting from a finite difference discretization of a coupled system of two linear stability equations, so the system is large…
Davide
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4
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2 answers
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 input. Is it possible to use the Eigtool my case…
Britomarti
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3
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What is the complexity of calculating K-th largest real part eigenvalue of non-normal sparse matrix
I just need to calculate the largest real part of eigenvalues of a Jacobian which is highly non-normal and singular. Most of the eigenvalues are negative, and some of them are positive but near to zero relatively. I want to find the largest one…
CatDog
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3
votes
2 answers
Using a subspace iteration method to obtain eigenvalues. Getting eigenvectors too but I don't understand why
I'm using an iterative subspace algorithm (dsrrit) to obtain the eigenvalues of an eigenvector equation
$$
-\nabla^2 \mathbf{x} = \lambda\mathbf{x}
$$
where $\nabla^2$ is the usual Laplacian operator. The algorithm returns a set of eigenvalues…
DJames
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2
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1 answer
Estimating the spectral radius when the dominant eigenvalues are complex conjugates
I want to determine the spectral radius of a large non-symmetric matrix $A$ whose dominant eigenvalues are a pair of complex conjugates. My first instinct was to use a power iteration with a starting vector $x$ in the complex plane. I do recall…
Paul
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0
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1 answer
Are there any constraints on eigenvalues that are used in inverse iteration?
What is the result of the method for multiple eigenvalues? Is there any case for which this method will not work altogether?
Maristo-Tero
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