Kernel-based methods milestones and new trends Stefano De Marchi, Francesco Marchetti, Emma Perracchione

Format:

Book

Author/Creator:

De Marchi, Stefano, 1973- author.

Marchetti, Francesco (Of Università di Padova), author.

Perracchione, Emma, author.

Series:

Cambridge monographs on applied and computational mathematics ; 46.

Cambridge monographs on applied and computational mathematics 46

Language:

English

Subjects (All):

Kernel functions.

Physical Description:

1 online resource

Place of Publication:

Cambridge Cambridge University Press 2026

Summary:

"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"-- Cambridge Core

Contents:

Positive definite kernels and functions

RBF interpolation and polynomial precision

Error estimates and examples of kernels

On uncertainty principles and shape parameter selection

Rational kernels

Partition of unity

Efficient reduced-basis approximation

Approximating via variably scaled discontinuous kernels

Application of VSDKs to magnetic particle imaging

Applications to astronomical imaging

Kernels in machine learning

Support vector machines and other methods

Local-to-global SVMs

Learning data-driven optimized kernels

Choosing and learning the scaling function for the VSKs

Kernels for persistent homology

Software

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (Cambridge Core, viewed August 13, 2026)

Other Format:

Print version De Marchi, Stefano, 1973- Kernel-based methods

ISBN:

9781009769105

1009769103

OCLC:

1579814480

Access Restriction:

Restricted for use by site license