[RFC] Add estimates of operator norms

[sethaxen]

This PR adds three methods:

• opnormest1(A): lower-bound estimate of opnorm(A, 1)
• opnormestprod1(As...)/opnormestprod1(A,p::Integer): lower-bound estimate of opnorm(prod(As), 1)
• opnormestinv1(A): lower-bound estimate of opnorm(inv(A), 1)

The implementation of opnormest1 comes from the paper by Higham and Tisseur. It is especially useful when computing the actions of matrix functions (e.g. exp(A)*b) for large and sparse A. Edit: It also works on any object that implements a minimal interface of a linear operator.

There was already an implementation of opnormestinv1 opnormest(inv, A, 1) (called opnormestinv(A)) in SparseArrays which served as the starting point for this implementation and is now superseded. From a quick scan, future PRs could make use of this estimate for computing condition numbers and for speeding up the matrix logarithm, which currently calls opnorm(A^p, 1) for powers of 1 through 5. Even for a dense A, the estimate is faster and on my machine gives a 20% speed-up for a large matrix. Edit: this implementation also minimizes the number of allocations, which causes a substantial speed-up

I've marked this as RFC because I'm not very satisfied with the interface thus far, in particular the interface to return vectors corresponding to the estimate (see docstrings).

Edit: I've added the opnormest function which is exported. The public interface is now:

• opnormest(A, p=2): estimate opnorm(A, p)
• opnormest(f, A, p=2): estimate opnorm(f(A), p) for certain f (pinv, inv, and prod already supported). While clean, this interface is not very extensible. e.g., if we want to support f(A) = A^n or f(A) = A^(-n), there's not an obvious existing f we can use (except maybe Base.Fix2, but we would need to add ^(n::Integer) = Base.Fix2(^, n) to make it user-friendly).

I also added a power iteration method for estimating the 2-norm, which I believe is the approach matlab's normest function uses.

Relates #12609, JuliaLang/LinearAlgebra.jl#232

[sethaxen]

These currently error. It doesn't seem that chaining @test_deprecated for these tests actually works.

[DilumAluthge]

@sethaxen It looks like this PR touches five files. Three of those files are in the LinearAlgebra stdlib, and the remaining two files are in the SparseArrays stdlib.

We have moved the SparseArrays stdlib to an external repository. Therefore, for the portion of this PR that modifies the SparseArrays stdlib, can you please:

1. Remove the SparseArrays changes from this PR.
2. Open a new PR against https://github.com/JuliaLang/SparseArrays.jl with the SparseArrays changes.

Thank you!

[DilumAluthge]

We have moved the LinearAlgebra stdlib to an external repo: https://github.com/JuliaLang/LinearAlgebra.jl

@sethaxen If you think that this PR is still relevant, please open a new PR on the LinearAlgebra.jl repo.