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# Questions tagged [perturbation]

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### Eigenvalues in matrix perturbation theory converge to wrong value?

Given a Hermitian matrix $H$ and let $\lambda_0^H$ is the minimum eigenvalue of $H$. To use perturbation theory to find $\lambda_0^H$, we can first start with splitting $H$ into something like the ...
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### Could variable be still function in x and y after performing Reynolds averaging over area

All, Let $S(x,y,t)$ be a variable function in $x$, $y$, and $t$. After performing Reynold averaging over area $\frac{1}{A}\int S(x,y,t) dA$, could $S$ still be a function in $x$, and $y$? Equations (1-...
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### Bounding eigenvalue/eigenspace perturbations for hermitian matrices

Let $H$ be a Hermitian $n \times n$ matrix. Let $V$ be another such matrix. For real $t$, let us consider the one-parameter family $$H(t) = H + t V$$ of Hermitian matrices. Kato's perturbation theory ...
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### Eigenvalues of a Symmetric Positive Semi-Definite (PSD) matrix after rank one update

I have a Symmetric Positive Semi-Definite matrix $A$ which i know its eigenvalue and eigenvectors. let $v$ and $u$ be a random column vector. i want to know if it is possible to have eigenvalues of ...
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### Adding a multiple of the Identity to a LU factorized matrix

Suppose a square, dense, symmetric matrix $A$ has been factorized into $L$ and $U$ components by performing a LU decomposition. Now let $B = A+\lambda I$. Is there any way to efficiently compute the ...
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### Where are the boundary layers?

I am learning perturbation theory and would like to be able to determine where boundary layers are going to occur just by looking at the differential equation. Let $n\in\mathbb{N}$ and $p_i(x)$, \$0\...
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