Ebook: Multivariate Polynomial Approximation

Multivariate polynomials are a main tool in approximation. The book begins with an introduction to the general theory by presenting the most important facts on multivariate interpolation, quadrature, orthogonal projections and their summation, all treated under a constructive view, and embedded in the theory of positive linear operators. On this background, the book gives the first comprehensive introduction to the recently developped theory of generalized hyperinterpolation. As an application, the book gives a quick introduction to tomography. Several parts of the book are based on rotation principles, which are presented in the beginning of the book, together with all other basic facts needed.

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Multivariate polynomials are a main tool in approximation. The book begins with an introduction to the general theory by presenting the most important facts on multivariate interpolation, quadrature, orthogonal projections and their summation, all treated under a constructive view, and embedded in the theory of positive linear operators. On this background, the book gives the first comprehensive introduction to the recently developped theory of generalized hyperinterpolation. As an application, the book gives a quick introduction to tomography. Several parts of the book are based on rotation principles, which are presented in the beginning of the book, together with all other basic facts needed.

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Multivariate polynomials are a main tool in approximation. The book begins with an introduction to the general theory by presenting the most important facts on multivariate interpolation, quadrature, orthogonal projections and their summation, all treated under a constructive view, and embedded in the theory of positive linear operators. On this background, the book gives the first comprehensive introduction to the recently developped theory of generalized hyperinterpolation. As an application, the book gives a quick introduction to tomography. Several parts of the book are based on rotation principles, which are presented in the beginning of the book, together with all other basic facts needed.

Content:
Front Matter....Pages i-x
Front Matter....Pages 1-1
Basic Principles and Facts....Pages 3-18
Gegenbauer Polynomials....Pages 19-38
Front Matter....Pages 39-39
Multivariate Polynomials....Pages 41-66
Polynomials on Sphere and Ball....Pages 67-108
Front Matter....Pages 109-109
Approximation Methods....Pages 111-178
Approximation on the Sphere....Pages 179-262
Approximation on the Ball....Pages 263-282
Front Matter....Pages 283-283
Tomography....Pages 285-303
Back Matter....Pages 305-358

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Multivariate polynomials are a main tool in approximation. The book begins with an introduction to the general theory by presenting the most important facts on multivariate interpolation, quadrature, orthogonal projections and their summation, all treated under a constructive view, and embedded in the theory of positive linear operators. On this background, the book gives the first comprehensive introduction to the recently developped theory of generalized hyperinterpolation. As an application, the book gives a quick introduction to tomography. Several parts of the book are based on rotation principles, which are presented in the beginning of the book, together with all other basic facts needed.

Content:
Front Matter....Pages i-x
Front Matter....Pages 1-1
Basic Principles and Facts....Pages 3-18
Gegenbauer Polynomials....Pages 19-38
Front Matter....Pages 39-39
Multivariate Polynomials....Pages 41-66
Polynomials on Sphere and Ball....Pages 67-108
Front Matter....Pages 109-109
Approximation Methods....Pages 111-178
Approximation on the Sphere....Pages 179-262
Approximation on the Ball....Pages 263-282
Front Matter....Pages 283-283
Tomography....Pages 285-303
Back Matter....Pages 305-358
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