Krylov 1.0

[abelsiqueira]

Epic created through ZenHub to control what is needed for the Krylov 1.0 release.

[amontoison]

Version 1.0

• [x] LNLQ (#128)
• [ ] USYMLQR (#164)
• [x] Regularization in CRAIG and CRAIGMR (#171)

Version ≥ 1.0

• [ ] Support for complex linear systems (#103)
• [ ] Use 5-arguments mul! (y <- a * A * v + b * y and z <- c * A' * u + c * z) to reduce the number of vectors allocated

[dpo]

I don't think we need complex systems for 1.0 but would be great to have at some point of course.

[RoyiAvital]

I'd add 2 features before 1.0.000:

1. A State of Solver An API to supply a state of solver (Probably the solver itself) to the in place flavor of functions too add more iterations. For instance, I ran a CG with 500 iterations and it didn't converge to the required tolerance. By using cg!() on the same solver with itmax = 1000 I expect it to apply another 1000 iterations from the last iteration.
2. User Supplied Initial Vector The user can supply the solvers (Or constructors) with initial guess. This is highly helpful when the user use the solvers in a loop with ever slightly changing RHS. So it makes sense to start from the solution of the previous run. See https://github.com/JuliaSmoothOptimizers/Krylov.jl/issues/414.

By the way, thank you for this package and Linear Operators. A really powerful combination,