Search results for "Power iteration"
showing 4 items of 4 documents
A Note on the Nonlinear Landweber Iteration
2014
We reconsider the Landweber iteration for nonlinear ill-posed problems. It is known that this method becomes a regularization method in the case when the iteration is terminated as soon as the residual drops below a certain multiple of the noise level in the data. So far, all known estimates of this factor are greater than two. Here we derive a smaller factor that may be arbitrarily close to one depending on the type of nonlinearity of the underlying operator equation.
A Singular Multi-Grid Iteration Method for Bifurcation Problems
1984
We propose an efficient technique for the numerical computation of bifurcating branches of solutions of large sparse systems of nonlinear, parameter-dependent equations. The algorithm consists of a nested iteration procedure employing a multi-grid method for singular problems. The basic iteration scheme is related to the Lyapounov-Schmidt method and is widely used for proving the existence of bifurcating solutions. We present numerical examples which confirm the efficiency of the algorithm.
Eigenvalues of non-hermitian matrices: a dynamical and an iterative approach. Application to a truncated Swanson model
2020
We propose two different strategies to find eigenvalues and eigenvectors of a given, not necessarily Hermitian, matrix (Formula presented.). Our methods apply also to the case of complex eigenvalues, making the strategies interesting for applications to physics and to pseudo-Hermitian quantum mechanics in particular. We first consider a dynamical approach, based on a pair of ordinary differential equations defined in terms of the matrix (Formula presented.) and of its adjoint (Formula presented.). Then, we consider an extension of the so-called power method, for which we prove a fixed point theorem for (Formula presented.) useful in the determination of the eigenvalues of (Formula presented…
Guaranteed error bounds for a class of Picard-Lindelöf iteration methods
2013
We present a new version of the Picard-Lindelof method for ordinary dif- ¨ ferential equations (ODEs) supplied with guaranteed and explicitly computable upper bounds of an approximation error. The upper bounds are based on the Ostrowski estimates and the Banach fixed point theorem for contractive operators. The estimates derived in the paper take into account interpolation and integration errors and, therefore, provide objective information on the accuracy of computed approximations. peerReviewed