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JuliaSmoothOptimizers / Krylov.jl

A Julia Basket of Hand-Picked Krylov Methods
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Lower bound of the backward error in MINRES and MINRES-QLP #687

Open amontoison opened 1 year ago

amontoison commented 1 year ago

The lower bound of the backward error in MINRES and MINRES-QLP is only correct without preconditioner. We should adapt the formula to handle preconditioners. Because it's a lower bound, we should also tune the tolerances. I used sqrt(eps(T)) three years to support multiprecision in all Krylov methods but It could probably be eps(T) for some stopping conditions.

amontoison commented 1 year ago

In single precision, we can easily see the problem with GPU tests (#699).