Questions tagged [high-dimensional]

A high-dimensionality space is one that can only be spanned by a basis set with a large number of elements. High-dimensional problems often suffer from the *Curse of Dimensionality*, which is exponential growth in the problem size as a function of the number of dimensions.

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3answers
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PDEs in Many Dimensions

I know that most methods of finding approximate solutions to PDEs scale poorly with the number of dimensions, and that Monte Carlo is used for situations that call for ~100 dimensions. What are good ...
5
votes
1answer
327 views

Working with multi-dimensional functions

How would you represent functions of type $[-1, 1]^n \to \mathbb R \;$ for moderate $n$? How would you integrate them? For small $n$ (1-2) such functions can be represented as histograms, vectors in ...
4
votes
1answer
130 views

Constructing the origin position by transforming distance information

Suppose a set of $n$ points, $n\in M$, is given in some $d-$dimensional space, $X\in\mathbb{R}^{n\times d}$. Among these $n$ points, some $k\in K$ are selected, so $k<n$, and the distances from ...