As an improved method of k-nearest neighbor classification, the local mean-based nonparametric classifier had the ability to resist the effects of noise and classify unbalanced data. When selecting the nearest k samples and calculating the distance between the test samples and the local mean-based vectors, it always used Euclidean distance. However, for multi-dimensional data, using Euclidean d...

During the past the convergence analysis for linear statistical inverse problems has mainly focused on spectral cut-off and Tikhonov type estimators. Spectral cut-off estimators achieve minimax rates for a broad range of smoothness classes and operators, but their practical usefulness is limited by the fact that they require a complete spectral decomposition of the operator. Tikhonov estimators...

Many physical problems are naturally formulated as nonlinear par-abolic systems of partial diierential equations in periodic geometry. In this paper, a simple, eecient, spectrally-accurate numerical method for these problems is described and implemented. The method combines stii extrapolation with fast solvers for elliptic systems. Theory and numerical results show that the method solves even d...