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Numerical algorithms for problems in analysis and algebra, scientific computation

3 votes
1 answer
73 views

How to deal with singularities in thin plate splines?

Follow up from this question Thin-Plate-Spline understanding and solution. In the general case of $\mathbb{R}^N$ the following problem (interpolant which minimizes the Thin Plate Energy, specifically …
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1 vote
0 answers
80 views

Can this problem be rephrased as optimization on a manifold?

I have question. I have a Riemmanian manifold $\mathcal{M}$, like an $n$-dimensional regular surface in $\mathbb{R}^n$. And I have a smooth scalar field defined on this manifold $f:\mathcal{M} \to \ma …
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0 votes
1 answer
120 views

Least square error problem ill conditioning

I am trying to understand why I am getting an almost singular matrix in a problem I have. The problem is a simple as $$ \min_{X \in \mathbb{R}^{m,n}} \left\lVert AX - B \right\rVert_F^2 $$ Obvioulsy i …
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