Subspace recycling iterative methods and other subspace augmentation schemes are a successful extension to Krylov in which is augmented with fixed spanned by vectors deemed be helpful accelerating convergence or conveying knowledge of the solution. Recently, survey was published, framework describing vast majority such proposed [Soodhalter et al., GAMM-Mitt., 43 (2020), Art. e202000016]. In man...

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...

We present a general framework for a number of techniques based on projection methods onàugmented Krylov subspaces'. These methods include the deeated GM-RES algorithm, an inner-outer FGMRES iteration algorithm, and the class of block Krylov methods. Augmented Krylov subspace methods often show a signiicant improvement in convergence rate when compared with their standard counterparts using the...

A new proof of a pathwise uniqueness result of Krylov and Röckner is given. It concerns SDEs with drift having only certain integrability properties. In spite of the poor regularity of the drift, pathwise continuous dependence on initial conditions may be obtained, by means of this new proof. The proof is formulated in such a way to show that the only major tool is a good regularity theory for ...

Article history: Received 7 December 2009 Received in revised form 16 July 2010 Accepted 1 August 2010 Available online 26 August 2010

where gij denotes the metric of M , g = det(gij) > 0 and φ ∈ C∞(∂Ω), ψ > 0 is C∞ with respect to (x, z, p) ∈ Ω̄× R× TxM , TxM denotes the tangent space at x ∈M . Monge-Ampère equations arise naturally from some problems in differential geometry. The Dirichlet problem in Euclidean space R has been widely investigated. In this case the solvability has been reduced to the existence of strictly conv...

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...