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Assuming the following equation has a solution, I'm interested in finding any concrete values of $x_{1},\dots x_{n},y_{1},\dots y_{n},c_{1},c_{2},R$ that fulfills it. $$ \begin{bmatrix} 1 & 1 \\ ...

Consider $n,d \in \mathbb{N}_{>0}$, there are many functions $y:\mathbb{N}^{n} \to \mathbb{R}$. Now for simplicity, we denote $y(\alpha)$ to be $y_{\alpha}$. Let $|\alpha| = \sum_{i=1}^{n}\alpha_{i}...

The best rank $r$ approximation to a given matrix $M$ in Frobenius norm, according to Eckart-Young theorem, is truncated SVD - just keep $r$ largest singular values. What if I need to construct best ...