Nyhet

Kernel-Based Methods

Milestones and New Trends

AvStefano De Marchi,Francesco Marchetti

Inbunden, Engelska, 2026

Del 46 i serien Cambridge Monographs on Applied and Computational Mathematics

915 kr

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Beskrivning

Kernel methods, with origins in the pioneering work of Mercer (1909), Bochner (1933), and Aronszajn (1950), have become central tools in modern mathematics and machine learning. This book explores their deep connections with approximation theory, highlighting both classical results and cutting-edge developments. Through clear explanations and illustrative examples, it guides readers from foundational concepts to contemporary applications, including computational methods and real-world problem solving. By bridging theory and practice, the text not only provides a rigorous understanding of kernels but also inspires further exploration and research. Suitable for students, researchers, and practitioners, it invites readers to engage with ongoing advances in this dynamic field and to contribute to its future growth.

Produktinformation

Utgivningsdatum:2026-11-30
Vikt:500 g
Format:Inbunden
Språk:Engelska
Serie:Cambridge Monographs on Applied and Computational Mathematics
Antal sidor:242
Förlag:Cambridge University Press
ISBN:9781009769129

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Mer om författaren

Stefano De Marchi is Full Professor of Numerical Analysis at the University of Padova. He has authored more than 150 publications and is the managing editor of the open-access journal Dolomites Research Notes on Approximation. He is the founder of the Italian Network on Approximation and one of the discoverers of the so-called Padua points. Francesco Marchetti is Assistant Professor of Numerical Analysis at the University of Padova. His research lies at the intersection of approximation theory and machine learning, focusing on kernel methods and polynomial and RBF interpolation, with applications to medical imaging and space weather forecasting, within national and international research projects. Emma Perracchione is Associate Professor at Politecnico di Torino. Her research focuses on approximation theory and its applications to solar physics, such as astronomical imaging. She is currently Principal Investigator of the GOSSIP project (Greedy Optimal Sampling for Solar Inverse Problems), funded by the Italian Ministry of Universities and Research.

Innehållsförteckning

List of illustrations; List of tables; 1. Introduction; 2. Positive deﬁnite kernels and functions; 3. RBF interpolation and polynomial precision; 4. Error estimates and examples of kernels; 5. On uncertainty principles and shape parameter selection; 6. Rational kernels; 7. Partition of Unity; 8. Efﬁcient reduced-basis approximation; 9. Approximating via variably scaled discontinuous kernels; 10. Application of VSDKs to magnetic particle imaging; 11. Applications to astronomical imaging; 12. Kernels in machine learning; 13. Support vector machines and other methods; 14. Local-to-Global SVMs; 15. Learning data-driven optimized kernels; 16. Choosing and learning the scaling function for the VSKs; 17. Kernels for persistent homology; 18. Software; 19. Conclusions; Bibliography; References; Index.