The Schwarz alternating algorithm, which is based on natural boundary element method, is constructed for solving the exterior anisotropic problem in the three-dimension domain. The anisotropic problem is transformed into harmonic problem by using the coordinate transformation. Correspondingly, the algorithm is also changed. Continually, we analysis the convergence and the error estimate of the ...

We consider adaptive identification algorithms based on hyperstability concepts with polyphase structures. The SPR condition required for convergence of these schemes can be always met by using a sufficiently high polyphase expansion factor M: The degree of persistent excitation required for parameter convergence is obtained. If some a priori knowledge about the system to identify is available,...

We present a mathematical analysis of the Wang-Landau algorithm, prove its convergence, and identify sources of errors and strategies for optimization. In particular, we found the histogram increases uniformly with small fluctuations after a stage of initial accumulation, and the statistical error is found to scale as square root of (ln f) with the modification factor f . This has implications ...

Based on numerical experiments with a cell-centred multigrid Poisson solver in one and two dimensions, we propose to use Alternating Coarse-Line Zebra ordering as a robust parallel smoother for the 2D case. The algorithm is presented based on a heuristic discussion, and the convergence rates obtained with diierent smoothers are compared. Local mode analysis is used to estimate the smoothing fac...

We derive a class of extended one-step methods of order m for solving delay-differential equations. This class includes methods of fourth and fifth order of accuracy. Also, the class of these methods depends on two free parameters. A convergence theorem and convergence factor of these methods are given. In addition, we investigate the stability properties of these methods. The results of the ar...

Convergence results are proved for a class of quadrature methods for integral equations of the form y(t) = fit) + /ô° k(t, s)y(s) ds. An important special case is the Nystrom method, in which the integral term is approximated by an ordinary quadrature rule. For all of the methods considered here, the rate of convergence is the same, apart from a constant factor, as that of the quadrature approx...

in this paper, several $delta$ and strong convergence theorems are established for the ishikawa iterations for nonexpansive mappings in the framework of cat(0) spaces. our results extend and improve the corresponding results

Sparse Bayesian factor models are routinely implemented for parsimonious dependence modeling and dimensionality reduction in highdimensional applications. We provide theoretical understanding of such Bayesian procedures in terms of posterior convergence rates in inferring high-dimensional covariance matrices where the dimension can be potentially larger than the sample size. Under relevant spar...