Reduce the cost of opnorm of B_k

[MohamedLaghdafHABIBOULLAH]

"It could be interesting to try other norms that are less expensive than the spectral norm, particularly the trace norm (the sum of eigenvalues when $B_k>0$)

[dpo]

The Frobenius norm is also interesting because $\Vert A \Vert_2 \leq \Vert A \Vert_F \leq \Vert A \Vert_*$, and it’s cheap to compute.

[dpo]

I think the convergence theory continues to hold if we compute any $\beta_k = \Theta(\Vert B_k \Vert)$, but we have to decide on how to compute $\beta_k$, especially for quasi-Newton operators.

[MohamedLaghdafHABIBOULLAH]

If we use the Frobenius norm, then we solve the allocation issue with opnrom.

[dpo]

But we don’t have it for quasi-Newton operators.

[MohamedLaghdafHABIBOULLAH]

Ok, I thought that we have norm for LinearOperators of all type...

[MohamedLaghdafHABIBOULLAH]

Otherwise, the trace norm if B_k is positive, and I believe that we can easily extract the diagonal

[dpo]

For the trace norm, we need the singular values. It's even costlier.

[MohamedLaghdafHABIBOULLAH]

Nope, if B_k is symmetric positive, then the trace norm is just the sum of its diagonal which is a norm!

[MaxenceGollier]

We should try to close this now to remove the allocations from R2N, @dpo you suggested using a Rayleigh quotient, can you try to implement it @MohamedLaghdafHABIBOULLAH ?