This work tackles the evaluation of a multigrid cycling strategy using inner flexible Krylov subspace iterations. It provides a valuable improvement to the Reitzinger and Schöberl algebraic multigrid method for systems coming from edgeelement discretizations.

We obtain boundary Hölder gradient estimates and regularity for solutions to the linearized Monge-Ampère equations under natural assumptions on the domain, Monge-Ampère measures and boundary data. Our results are affine invariant analogues of the boundary Hölder gradient estimates of Krylov.

The A-gradient minimization of the Rayleigh quotient allows to construct robust and fastconvergent eigensolvers for the generalized eigenvalue problem for (A,M) with symmetric and positive definite matrices. The A-gradient steepest descent iteration is the simplest case of more general restarted Krylov subspace iterations for the special case that all step-wise generated Krylov subspaces are tw...

A High Performance Computing alternative to traditional Krylov subspace methods, pipelined Krylov subspace solvers offer better scalability in the strong scaling limit compared to standard Krylov subspace methods for large and sparse linear systems. The typical synchronization bottleneck is mitigated by overlapping time-consuming global communication phases with local computations in the algori...

We present a framework for interpolatory model reduction that treats systems having a generalized coprime factorization C(s) (s)−1B(s) + D. This includes rational Krylov-based interpolation methods as a special case. The broader framework allows retention of special structure in reduced models such as symmetry, secondand higher order structure, state constraints, internal delays, and infinite d...

We consider proximinality and transitivity of proximinality for subspaces of finite codimen-sion in generalized direct sums of Banach spaces. We give several examples of Banach spaces where proximinality is transitive among subspaces of finite codimension. 1. Introduction. Let X be a Banach space and let Y be a closed subspace of X. We recall that Y is said to be a proximinal subspace of X if f...

Article history: Received 10 September 2014 Received in revised form 19 May 2015 Accepted 4 July 2015 Available online 10 July 2015

We give a concise introduction to some recent developments of Krylov subspace methods (in particular, the method of minimal residuals) and tendencies in the design and analysis of good preconditioners.

= 1 with convex level set {λ | σ2 (λ) = 1} . However the ellipticity is not uniform even under the strict convexity assumption on u, Du > 0. The standard Evans-Krylov-Safonov theory does not apply. To apply this theory, we make a Legendre-Lewy type transformation of the solution u so that the new function has bounded Hessian (Step 1); the new corresponding equation is convex (only under the par...