The Origin and Development of Krylov Subspace Methods

Avoiding Krylov Subspace Methods

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Communication-avoiding Krylov subspace methods

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Krylov subspace methods in the electronic industry

Krylov subspace methods for the Dirac equation

The Lanczos algorithm is evaluated for solving the time-independent as well as the time-dependent Dirac equation with arbitrary electromagnetic fields. We demonstrate that the Lanczos algorithm can yield very precise eigenenergies and allows very precise time propagation of relativistic wave packets. The unboundedness of the Dirac Hamiltonian does not hinder the applicability of the Lanczos alg...

Krylov subspace methods and minimal residuals

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.