# Questions tagged [total-variation]

This tag is for questions relating to Total Variation.The concept of total variation for functions of one real variable was first introduced by Camille Jordan in the paper (Jordan 1881). He used the new concept in order to prove a convergence theorem for Fourier series of discontinuous periodic functions whose variation is bounded. The extension of the concept to functions of more than one variable however is not simple for various reasons.

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### How this variational derivative is calculated?

In this paper https://arxiv.org/pdf/1907.09605.pdf \ let $\Omega \subset \mathbb{R}^n$ with $n \geq 1$ be a bounded Lipschitz domain with boundary $\partial \Omega$, $f: \Omega \rightarrow \mathbb{R}$ ...
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### Total Variation Distance of Normal Approximation for a Poisson 100.

Ross and Pekoz's book A Second Course in Probability gives the following question in their chapter on Stein-Chen Method: Compute a bound on the accuracy of a normal approximation for a Poisson random ...
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### How can we calculate the Euler-lagrange equations?

In this paper https://arxiv.org/pdf/1907.09605.pdf \ let $\Omega \subset \mathbb{R}^n$ with $n \geq 1$ be a bounded Lipschitz domain with boundary $\partial \Omega$, $f: \Omega \rightarrow \mathbb{R}$ ...
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### Relationship between limit and total variation

Consider a twice continuously differentiable and bounded function $f:\mathbb R \rightarrow \mathbb R$ has the following property: in any neighborhood of $\infty$, there are an infinite number of ...
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### Fréchet derivative of the total variation norm for measures on a manifold

Let $\Theta$ be a compact $d$-dimensional Riemannian manifold without boundary and $M(\Theta)$ (resp. $M_+(\Theta)$) denote the set of signed (resp. nonnegative) finite Borel measures on $\Theta$. ...
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### Does the derivative of a vector-valued BV function $f(x)$ equal to the norm of $f'(x)$?
Let $f(x)$ be a real-valued function on $[a,b]$ of bounded variation. It is standard that $f(x)$ is almost everywhere differentiable, and that $\dfrac{{\rm d}}{{\rm d}x} V^x_a f = |f'(x)|$ for a.e. \$x\...