[algorithms.eigs] add implicitly restarted arnoldi method

[lbalicki]

I implemented the implicitly restarted arnoldi method for computing a few eigenvalues of a real Operator. This is related to the issues #774 and #772.

[sdrave]

@lbalicki, @pmli, what is the status of this PR? Looks fairly mature. @lbalicki, you should probably rebase on master to get CI running again.

[pmli]

I still want to try it on some benchmarks.

[pmli]

I've tried eigs on a few SLICOT benchmarks and it works as good as I would have expected, i.e., very good for eigenvalues far from zero and not so good otherwise.

Below are some comments just from looking at the docstring.

Similar to the samdp module, it might be good to add some isinstance assertions in the eigs function and make other functions private (also, it would be good to write QR_iteration in lowercase).

[lbalicki]

I made the changes and also added myself to AUTHORS.md. For eigenvalues that are close to zero I will probably add a shift and invert option sometime in the near future.

[renefritze]

This'll need another rebase on master after #922 got merged for some CI fixes. Again. Sorry.

[codecov]

Codecov Report

Merging #880 into master will increase coverage by 0.02%.
The diff coverage is n/a.

Impacted Files	Coverage Δ
src/pymor/vectorarrays/numpy.py	84.31% <0.00%> (+0.73%)	⬆️

[pmli]

Thanks @lbalicki, here are a few more comments. I would be for merging after resolving these.

[sdrave]

I did not check the algorithm itself. Apart from a few minor comments, everything looks great!

[sdrave]

I think we can merge this now ..

[pmli]

Agreed. Thanks @lbalicki.