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Results tagged with computational-complexity
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user 11236
This is a branch that includes: computational complexity theory; complexity classes, NP-completeness and other completeness concepts; oracle analogues of complexity classes; complexity-theoretic computational models; regular languages; context-free languages; Komolgorov Complexity and so on.
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Do Isometry Groups Tell Us How Difficult Norms are to Compute?
The question: Consider two norms N1 and N2 on the space of n-by-n complex matrices. N1 and N2 have the same isometry group and computing N1 is NP-HARD. Does it follow that computing N2 is NP-HARD as w …
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Complexity of solving $\sum_i A_i X B_i = C$
This is exactly equivalent to asking the complexity of solving $\Phi(X) = C$, where $\Phi$ is a linear transformation acting on the vector space of $d \times d$ matrices. Since that vector space is $d …
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How hard (P, NP, NP-hard) is it to compute Schur norms of matrices (as multipliers)?
It turns out that this norm can be computed efficiently (i.e., it is in $P$). This wasn't known at the time that the Davidson paper (originally linked in a comment above) was written, which is why it …
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NP-hard problems in linear algebra and real analysis
The tensor product has a way of making easy problems into (NP-)hard problems. Rank of a 2-tensor (matrix)? Easy. Rank of a 3-tensor? NP-hard. Spectral norm of a matrix? Easy. Spectral norm of a 3-tens …