The regularization tag has no wiki summary.

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votes

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### double integral and Hadamard finite part

Given the divergent integral
$$ \int _{0}^{\infty}dx \int_{0}^{\infty}dy \frac{x^{2}y+1}{1+x+y} $$
how can I apply Hadamard's finite part to give a finite meaning to it ?
It is just made by ...

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votes

**1**answer

80 views

### General method for under and over determined systems?

Suppose I have a system:
$$
Ax = b
$$
where $A$ is a $m$ by $n$ matrix which is less than full rank (neither full column nor row rank). In my particular case $m<n$.
I'd like a combination of a ...

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votes

**0**answers

67 views

### Inverse problem with a rank-1 update

I hope you can help me out with this. I have to find the solution x to an inverse system
$$
x=A^{-1}b
$$
This inverse problem is basically a least square problem with a rank-1 update.
$$
...

**5**

votes

**1**answer

284 views

### What are some geometric / physical / probabilistic interpretations of the Riemann zeta function at integer arguments n ≤ 1?

Introduction: This is slightly edited and generalised version of a question I asked on the Physics Stack Exchange website. This question has a twin brother asked here on MO, only now we consider ...

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votes

**2**answers

290 views

### Choosing the order of Tikhonov regularization of an inverse problem

This question is migrated from math.stackexchange.
Let me first describe the problem I am trying to solve and then the question I have. I greatly appreciate anyone who can shine some light on it.
...

**21**

votes

**3**answers

2k views

### Understanding zeta function regularization

I attended a talk this morning on Ray-Singer torsion, in which Rafael Siejakowski introduced zeta function regularization in a compelling way. The goal is to define the determinant of a positive ...

**2**

votes

**1**answer

333 views

### Regularization of Zygmund functions

Dear community.
I would like to derive a "good" estimate on $\frac{d}{dt}f_\epsilon(t)$, where $f_\epsilon$ is a regularization of a Zygmund-continuous function $f$, i.e.
...

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votes

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600 views

### Nonlinear circle fit with known radius

I have data points from a half circle and I already know the approximate radius. I want to find the circle which best fits the points using a fixed radius. How can I do this? If I solve the problem ...

**2**

votes

**1**answer

302 views

### What is the regularity of the argument of a complex function?

Let $\psi=f+ig=\rho e^{i\theta}$ be a complex function on some open subset of $\mathbb{R}^n$, where $f,g,\rho$ and $\theta$ are real-valued. I happened to find that the identity of differentiation for ...

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votes

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521 views

### What's the correct notion of determinant of a bilinear pairing?

By a pairing on a vector space $V$, I mean a linear map $A : V \otimes V \to R$. If $V$ is $n$-dimensional ($n < \infty$), then I can define the determinant of $A$ by considering the canonical ...

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votes

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2k views

### Zeta-function regularization of determinants and traces

The short answer to my question may be a pointer to the right text. I will give all the background I know, and then ask my questions in list form.
Let A be an operator (on an infinite-dimensional ...