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Kernel-algorithms in frame-approximations
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DOI：10.1016/j.exmath.2024.125583.png)
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Abstract
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With view to applications, we present here general classes of non-orthogonal expansions in Hilbert space. 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 work includes a diverse list of optimization problems, new Karhunen-Lo & egrave;ve transforms, and Principal Component Analysis (PCA) for digital images. A key feature of our algorithms is our use of recursive systems of projection operators. For this we also make use of specific reproducing kernel Hilbert spaces, kernel factorizations, 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. (c) 2024 Elsevier GmbH. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Keywords:
Positive-definite kernels
Reproducing kernel Hilbert spaces
Interpolation
Sampling
Frames
Optimization
Journal
E
IF:
0.9
Papers:
43
Citations:
0
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