Questions tagged [spectral]

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About some possible optimality properties of Ramanujan graphs

The Ramanujan graphs are optimal from the Alon-Bopanna point of view but.. Is there any sense in which one can call Ramanujan graphs to be the "optimal" spectral sparsifiers? (Reference : http://...
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About the sparsest-cut question

Can someone kindly help clarify as to exactly what is the generally accepted definition of the "sparsest cut" problem for a graph? (Isn't the set which achieves the Cheeger constant for a ...
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Finding the closest subspace to a collection of subspaces

Suppose we have a collection of linear subspaces $\mathbb{C}$ lying in $\mathbb{R}^d$, such that each $c \in \mathbb{C}$ is of dimension at most $k \leq d$ for a given fixed $k$ and $|\mathbb{C}| = n$....