Krylov subspace methods for the Dirac equation

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...

Avoiding Krylov Subspace Methods

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Communication-avoiding Krylov subspace methods

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Krylov subspace methods for solving linear systems

Krylov Subspace Methods for Tensor Computations

A couple of generalizations of matrix Krylov subspace methods to tensors are presented. It is shown that a particular variant can be interpreted as a Krylov factorization of the tensor. A generalization to tensors of the Krylov-Schur method for computing matrix eigenvalues is proposed. The methods are intended for the computation of lowrank approximations of large and sparse tensors. A few nume...