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

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

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...

On the Occurrence of Superlinear Convergence of Exact and Inexact Krylov Subspace Methods

Krylov subspace methods often exhibit superlinear convergence. We present a general analytic model which describes this superlinear convergence, when it occurs. We take an invariant subspace approach, so that our results apply also to inexact methods, and to non-diagonalizable matrices. Thus, we provide a unified treatment of the superlinear convergence of GMRES, Conjugate Gradients, block vers...

On the Superlinear Convergence of Exact and Inexact Krylov Subspace Methods

We present a general analytical model which describes the superlinear convergence of Krylov subspace methods. We take an invariant subspace approach, so that our results apply also to inexact methods, and to non-diagonalizable matrices. Thus, we provide a unified treatment of the superlinear convergence of GMRES, Conjugate Gradients, block versions of these, and inexact subspace methods. Numeri...

Preconditioned Krylov Subspace Methods for Eigenvalue Problems