We design and implement the first polynomial-based spectral method on graphic processing units (GPUs). The key to success lies in the seamless integration of the matrix diagonalization technique and new generation CUDA tools. The method is applicable to elliptic equations with general boundary conditions in both 2-D and 3-D cases. We show remarkable speedups of more than 10 times in the 2-D cas...

Solutions to linear inverse problems on the sphere, common in geodesy and geophysics, are compared for Tikhonov's method of regularization, Wiener filtering and spectral smoothing and combination as well as harmonic analysis. It is concluded that Wiener and spectral smoothing, although based on different assumptions and target functions, yield the same estimator. Also, provided that the extra i...

The analysis of spectral data constitutes new challenges for machine learning algorithms due to the functional nature of the data. Special attention is given to the used metric in such analysis. Recently a prototype based algorithm has been proposed which allows the integration of a full adaptive matrix in the metric. In this contribution we analyse this approach with respect to band matrices a...

Abstract We review our recent results on pseudo-hermitian random matrix theory which were hitherto presented in various conferences and talks. (Detailed accounts of work will appear soon separate publications.) Following an introduction this new type matrices, we focus two specific models matrices are with respect to a given indefinite metric B. Eigenvalues either real, or come complex-conjugat...

We present a numerical scheme for determining hyperboloidal initial data sets for the conformal field equations by using pseudo-spectral methods. This problem is split into two parts. The first step is the determination of a suitable conformal factor which transforms from an initial data set in physical space-time to a hyperboloidal hypersurface in the ambient conformal manifold. This is achiev...

Abstract With the rapid development of information technology, a large amount unlabeled high-dimensional data has been generated. To be able to better handle these data, we propose new self-supervised feature selection algorithm for spectral embedding based on block HSIC lasso (FSSBH). It innovatively applies theoretical approach scenarios importance assessment, and performs by learning with ps...