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The Christoffel Darboux Kernel for Data Analysis Cambridge Monographs on Applied and Computational Mathematics 1st Edition by Jean Bernard Lasserre, Edouard Pauwels, Mihai Putinar ISBN 1108838065 9781108838061

Name: The Christoffel Darboux Kernel for Data Analysis Cambridge Monographs on Applied and Computational Mathematics 1st Edition by Jean Bernard Lasserre, Edouard Pauwels, Mihai Putinar ISBN 1108838065 9781108838061
SKU: EB-51992566
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The Christoffel Darboux Kernel for Data Analysis Cambridge Monographs on Applied and Computational Mathematics Jean Bernard Lasserre Digital Instant Download

Author(s): Jean Bernard Lasserre, Edouard Pauwels, Mihai Putinar

ISBN(s): 9781108838061, 1108838065

Edition: New

File Details: PDF, 5.19 MB

Year: 2022

Language: English

SKU: EB-51992566 Category: Uncategorized Tags: Edouard Pauwels, Jean Bernard Lasserre, Mihai Putinar

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The Christoffel Darboux Kernel for Data Analysis Cambridge Monographs on Applied and Computational Mathematics 1st Edition by Jean Bernard Lasserre, Edouard Pauwels, Mihai Putinar – Ebook PDF Instant Download/Delivery: 1108838065, 9781108838061
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ISBN 10: 1108838065
ISBN 13: 9781108838061
Author: Jean Bernard Lasserre, Edouard Pauwels, Mihai Putinar

The Christoffel–Darboux kernel, a central object in approximation theory, is shown to have many potential uses in modern data analysis, including applications in machine learning. This is the first book to offer a rapid introduction to the subject, illustrating the surprising effectiveness of a simple tool. Bridging the gap between classical mathematics and current evolving research, the authors present the topic in detail and follow a heuristic, example-based approach, assuming only a basic background in functional analysis, probability and some elementary notions of algebraic geometry. They cover new results in both pure and applied mathematics and introduce techniques that have a wide range of potential impacts on modern quantitative and qualitative science. Comprehensive notes provide historical background, discuss advanced concepts and give detailed bibliographical references. Researchers and graduate students in mathematics, statistics, engineering or economics will find new perspectives on traditional themes, along with challenging open problems.

The Christoffel Darboux Kernel for Data Analysis Cambridge Monographs on Applied and Computational Mathematics 1st Table of contents:

Part I: Historical and Theoretical Background

Chapter 2: Positive definite kernels and moment problems
Chapter 3: Univariate Christoffel–Darboux analysis
Chapter 4: Multivariate Christoffel–Darboux analysis
Chapter 5: Singular supports

Part II: Statistics and Applications to Data Analysis

Chapter 6: Empirical Christoffel–Darboux analysis
Chapter 7: Applications and occurrences in data analysis

Part III: Complementary Topics

Chapter 8: Further applications
Chapter 9: Transforms of Christoffel–Darboux kernels
Chapter 10: Spectral characterization and extensions of the Christoffel function