# 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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### Methods to approximate obective function gradients from point cloud

Problem statement: Assume that I have an objective function $f(x)$ which takes as input a $D$-dimensional vector $x\in\mathbb{R}^D$, and that $f(x)$ is sufficiently smooth. Assume further that I ...
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### Numerical solution to N-dimensional diffusion on simplex?

Assume I have a system of at least (but generally only) $N+1$ points in an $N$-dimensional space ($N > 3$ is possible). At each of these points $x_i, i=1,...,N+1$ I know an initial potential/...
Suppose a configuration $X\in\mathbb{R}^{n\times 2}$ is output of PCA on some high-dimensional data $Y\in\mathbb{R}^{n\times h}$. Note that this PCA is performed by $$X=Y\cdot U,$$ where columns of $U$...
I have a large system of boundary value problems of the form $$\frac{d^2 y }{dt^2} = C(t) y + b(t),$$ where the variable $y$ is a vector that has anywhere from 50 to around 500 components, $C$ is a ...