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Connection of eigenspace of finite Hilbert matrix and its continuous operator counterpart

I am trying to understand the connection between the eigenspace of the continuous operator $$ H(x,y) = \frac{1}{x+y} $$ which is nothing but the square of the Laplace operator, and its discrete ...
knuth's user avatar
  • 33
4 votes
1 answer
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complexity of computing the singular vector corresponding to the smallest singular value

It is known that the singular value decomposition of an $m \times n$ matrix $A$ is in general of complexity of the order $m n^2$, assuming that $m \ge n$. But what if we only want to compute say the ...
Manos's user avatar
  • 398
1 vote
0 answers
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Generalized eigenvalue problem with nonnegative eigenvector constraint

Consider the following problem that is known to be non-convex but can be solved as a generalized eigenvalue problem (i.e. has a global optimum solution): $\underset{w}{\text{maximize}}\quad w^{\top}...
Majid's user avatar
  • 11