In this note a theoretical analysis of some Krylov subspace approximations to the matrix exponential operation $\exp (A)v$ is presented, and a priori and a posteriors error estimates are established.… Expand

In this paper, several implementations of Newton-like iteration schemes based on Krylov subspace projection methods for solving nonlinear equations are considered.Expand

IEEE Transactions on Pattern Analysis and Machine…

1 December 2007

TLDR

We propose a method, named orthogonal neighborhood preserving projections, which works by first building an "affinity" graph for the data in a way that is similar to the method of locally linear embedding (LLE).Expand

Some algorithms based upon a projection process onto the Krylov subspace K/sub m/ = Span(r/sub 0/, Ar/sub 0/,..., A/sup m-1/r/sub 0/) are developed, generalizing the method of conjugate gradients to… Expand

Incomplete LU factorization preconditioners have been surprisingly successful for many cases of general nonsymmetric and indefinite matrices. However, their failure rate is still too high for them to… Expand

Abstract It is shown that the method of Arnoldi can be successfully used for solvinglarge unsymmetric eigenproblems. Like the symmetric Lanczos method, Arnoldi's algorithm realizes a projection… Expand