Biorthogonal rational Krylov subspace methods

Avoiding Krylov Subspace Methods

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Communication-avoiding Krylov subspace methods

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Convergence analysis of Krylov subspace methods †

One of the most powerful tools for solving large and sparse systems of linear algebraic equations is a class of iterative methods called Krylov subspace methods. Their significant advantages like low memory requirements and good approximation properties make them very popular, and they are widely used in applications throughout science and engineering. The use of the Krylov subspaces in iterati...

Stability of Krylov Subspace Spectral Methods

This talk summarizes recent analysis of an alternative approach to the solution of diffusion problems and wave propagation problems in the variable-coefficient case that leads to a new class of numerical methods, called Krylov subspace spectral methods [3]. The basic idea behind these methods, applied to a PDE of the form du/dt + L(x,D)u = 0, is to use Gaussian quadrature in the spectral domain...

Krylov subspace methods for solving linear systems