# Questions tagged [inverse-problems]

Inverse problems involve for example reconstruction of an object based on physical measurements and finding a best model/parameters out of a family given observed data. Typically the corresponding "forward" problems are well-posed and can be solved straightforwardly, while the inverse problems are often ill-posed. Not to be confused with the (inverse) tag.

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### Reconstruction of second-order elliptic operator from spectrum

Let $M$ be a compact smooth manifold, $(\lambda_n)_{n=1}^{\infty}$ be a square-summable monotonically increasing sequence of non-negative numbers, and let $(f_k)_{k=1}^{\infty}$ be continuous ...
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### Implicit function theorem / Implicit selections when Jacobian not invertible

I saw the attached result in the book by Dontchev and Rockafellar. It requires the Jacobian to be of full rank m. I suspect this condition can be further relaxed. Assume that we know that the columns ...
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### Reference request: diffusion approximation to the radiative transport

I'm looking for a good, modern reference for the diffusion approximation to the radiative transport problem. I'm aware of the text of Dautray and Lions, as well as the monograph by Bensoussan, Lions, ...
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Let $f$ be a compactly supported function in $\Omega \subset \mathbb{R}^3$ and $\Delta u=f$ in $\Omega$ such that $D^{\alpha}u=0$ on $\partial \Omega$ for every multi-index $\alpha$ with $|\alpha| \... 1 vote 0 answers 113 views ### On the Integration and Manipulation of Expressions Involving Hypergeometric Functions I would like to ask the following two: For the integral: \begin{equation} \int_{0}^{t}\left( 1-s^p \right)^{\frac{1-p}{p}}ds \end{equation} I know that it is reduced to the following product ... 3 votes 1 answer 540 views ### Is this result on an unconstrained inverse quadratic programming problem new or known already? Is this problem and solution actually new, or has someone done this earlier? The details can be found in the preprint: arxiv:1701.01477. Let us consider a direct quadratic programming problem: $$\... 6 votes 2 answers 810 views ### Approximating Uniform Distribution with Mixture of Gaussians Let T be a compact, connected, proper subset of \mathbb{R}^3:\quad T \subset \mathbb{R}^3. Further let \left\{ \boldsymbol{\mu}_i \right\}_{i=1}^n be a given finite set of n point in T:$$ \... 4 votes 0 answers 411 views ### A question in inverse Galois Theory Let$\mathbb{G}= \{g_1,\cdots,g_n\}$be a finite group ,$\rho$be the regular representation. Let$x_1,\cdots,x_n$be indeterminates and let$x = (x_1,\cdots,x_n)^\top$. Let the matrix$G\$ be defined ... 677 views

### How to find Suleimanova's work on the Nonnegative Inverse Eigenvalue Problem?

Many papers cite the work of Suleimanova when studying inverse eigenvalue problems - in particular, the nonnegative inverse eigenvalue problem (NIEP). However, I cannot seem to find her work anywhere....
Suppose that we have Galois covering $$X\longrightarrow P^{1}_{\mathbb{Q}}$$ defined over the rationals which is cyclic, in the sense that the Galois group associated to the covering is a cyclic group....