Questions tagged [perturbation]

The tag has no usage guidance.

11 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
6 votes
0 answers
314 views

What is the technical difference between a deformation and a perturbation?

What is the technical difference between a deformation and a perturbation? Do they exist in somewhat different categories?
Jim Stasheff's user avatar
  • 3,840
4 votes
0 answers
80 views

Perturbation of a rank-restricted product of matrices

I formulated a statement, which is hopefully true (at least I'm not knowledgeable enough to see a reason for it not to be). However, I'm struggling to come up with a proof. Let $W_i \in \mathbb{R}^{...
Serghei's user avatar
  • 41
3 votes
0 answers
514 views

A question about the generalized Lidskii-Wielandt inequality for matrices proved by Thompson and Freede

In 1971, Thomson and Freede generalized the Lidskii-Wielandt inequalites as follows (version for singular values) Let $A$, $B$ be $n\times n$ Hermitian matrices. Suppose $\alpha_1\geq \alpha_2 \geq \...
user11870's user avatar
  • 227
2 votes
0 answers
75 views

Two-variable singular perturbation analysis

I am having difficulty with a two-variable singular perturbation analysis on a set of ODE's. The key difficulty is also present in the following, embarrassingly simple problem: If $x\sim \mathcal{O}(...
tom's user avatar
  • 131
2 votes
0 answers
861 views

Error bound on matrix vector multiplication

I am multiplying a matrix $A$ with vector $p$. However, the matrix $A$ isn't accurate. Some (a very small fraction) of the element's value is changed from $a_{i,j}$ to {0,$-a_{i,j}$, $2a_{i,j}$}. ...
arbitUser1401's user avatar
2 votes
0 answers
124 views

Perturbation analysis for three term recurrences

Jacobi polynomials, denoted by $J^{(\alpha,\beta)}_n$, on $[-1,1]$ satisfy a three term recurrence $$ J_{n+1}^{(\alpha,\beta)}(x) = (A_n+B_nx)J^{(\alpha,\beta)}_n + C_nJ_{n-1}^{(\alpha,\beta)}(x), \...
alext87's user avatar
  • 3,157
1 vote
0 answers
174 views

Coefficient perturbations of polynomials with real roots only

Let \begin{align} P(x) &= x^n+a_{n-1} x^{n-1} +\ldots+a_0 = \prod_{i=1}^n (x-p_i)\\ Q(x) &= x^n + b_{n-1} x^{n-1} + \ldots +b_0 = \prod_{i=1}^n (x-q_i)\\ p_i, q_i& \in \mathbb{R},\ 0<...
vkonton's user avatar
  • 175
1 vote
0 answers
294 views

Perturbation method of a boundary value problem

Let $u(x, \epsilon, \theta)$ be the solution of $$u''+(\epsilon \cos(x)+\theta-u)u=0$$ with boundary conditions $u'(0)=0$ and $u'(\pi)=0$. Here $\theta\in [0, 1]$. I tried to put the solution in ...
user62650's user avatar
1 vote
0 answers
203 views

Non-linear Perturbation Operator Examples

Consider a non-linear operator $\cal H$ which maps a function to a function (e.g., a map from a starting wave function $f(x,y,z)$ to a later wave function according to some non-linear PDE) and an $\...
bobuhito's user avatar
  • 1,537
1 vote
0 answers
212 views

componentwise eigenvector perturbation

Does the sin-theta theorem imply a componentwise nonasymptotic bound for eigenvectors? Assume, for the purpose of this question, that the eigenvalues concerned are simple. If this is trivial, I ...
Felix Goldberg's user avatar
0 votes
0 answers
47 views

Induced higher Gershgorin estimate

I have a problem which I suspect appears in literature under a name I haven't found yet. Let $H:\ell^2(\mathbb{Z}^2)\to \ell^2(\mathbb{Z}^2)$ given by $H=\Delta + D$, where $\Delta$ is the graph ...
Keen-ameteur's user avatar