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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.
5
votes
How to find Suleimanova's work on the Nonnegative Inverse Eigenvalue Problem?
A multiset of real numbers $\Lambda = \{\lambda_1,\dots,\lambda_n\}$ is called a Suleĭmanova spectrum if $\Lambda$ contains one positive element and $\sum_{i=1}^n \lambda_i \geq 0$.
Suleĭmanova [Dokla …
3
votes
Are inverse eigenvalue problems (IEPs) hopeless and not a fruitful area of research?
Although I work exclusively on the nonnegative inverse eigenvalue problem (NIEP), I can assure you that IEPs are far from dead, both on the theoretical side and the applied side (there has been a flur …