ﻻ يوجد ملخص باللغة العربية
The main purpose of our paper is a new approach to design of algorithms of Kaczmarz type in the framework of operators in Hilbert space. Our applications include a diverse list of optimization problems, new Karhunen-Lo`eve transforms, and Principal Component Analysis (PCA) for digital images. A key feature of our algorithms is our use of recursive systems of projection operators. Specifically, we apply our recursive projection algorithms for new computations of PCA probabilities and of variance data. For this we also make use of specific reproducing kernel Hilbert spaces, factorization for kernels, and finite-dimensional approximations. Our projection algorithms are designed with view to maximum likelihood solutions, minimization of cost problems, identification of principal components, and data-dimension reduction.
We establish a duality for two factorization questions, one for general positive definite (p.d) kernels $K$, and the other for Gaussian processes, say $V$. The latter notion, for Gaussian processes is stated via Ito-integration. Our approach to facto
For the interpolation of graph signals with generalized shifts of a graph basis function (GBF), we introduce the concept of positive definite functions on graphs. This concept merges kernel-based interpolation with spectral theory on graphs and can b
The present paper presents two new approaches to Fourier series and spectral analysis of singular measures.
With view to applications in stochastic analysis and geometry, we introduce a new correspondence for positive definite kernels (p.d.) $K$ and their associated reproducing kernel Hilbert spaces. With this we establish two kinds of factorizations: (i)
We give explicit transforms for Hilbert spaces associated with positive definite functions on $mathbb{R}$, and positive definite tempered distributions, incl., generalizations to non-abelian locally compact groups. Applications to the theory of exten