Krylov subspace methods for estimating operator-vector multiplications in Hilbert spaces

Avoiding Krylov Subspace Methods

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Operator-valued bases on Hilbert spaces

In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...

Numerical Methods for the QCD Overlap Operator: II. Optimal Krylov Subspace Methods

We investigate optimal choices for the (outer) iteration method to use when solving linear systems with Neuberger’s overlap operator in QCD. Different formulations for this operator give rise to different iterative solvers, which are optimal for the respective formulation. We compare these methods in theory and practice to find the overall optimal one. For the first time, we apply the so-called...

Superlinear Convergence of Krylov Subspace Methods for Self-Adjoint Problems in Hilbert Space

Communication-avoiding Krylov subspace methods

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