Advanced Problems In Constructive Approximation

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Constructive Approximation

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Author : George G. Lorentz
language : en
Publisher: Springer
Release Date : 1996-05-14

Constructive Approximation written by George G. Lorentz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-05-14 with Mathematics categories.

In the last 30 years, Approximation Theory has undergone wonderful develop ment, with many new theories appearing in this short interval. This book has its origin in the wish to adequately describe this development, in particular, to rewrite the short 1966 book of G. G. Lorentz, "Approximation of Functions." Soon after 1980, R. A. DeVore and Lorentz joined forces for this purpose. The outcome has been their "Constructive Approximation" (1993), volume 303 of this series. References to this book are given as, for example rCA, p.201]. Later, M. v. Golitschek and Y. Makovoz joined Lorentz to produce the present book, as a continuation of the first. Completeness has not been our goal. In some of the theories, our exposition offers a selection of important, representative theorems, some other cases are treated more systematically. As in the first book, we treat only approximation of functions of one real variable. Thus, functions of several variables, complex approximation or interpolation are not treated, although complex variable methods appear often.

Constructive Approximation

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Author : George G. Lorentz
language : en
Publisher: Springer
Release Date : 1996

Constructive Approximation written by George G. Lorentz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.

In the last 30 years, Approximation Theory has undergone wonderful develop ment, with many new theories appearing in this short interval. This book has its origin in the wish to adequately describe this development, in particular, to rewrite the short 1966 book of G. G. Lorentz, "Approximation of Functions." Soon after 1980, R. A. DeVore and Lorentz joined forces for this purpose. The outcome has been their "Constructive Approximation" (1993), volume 303 of this series. References to this book are given as, for example rCA, p.201]. Later, M. v. Golitschek and Y. Makovoz joined Lorentz to produce the present book, as a continuation of the first. Completeness has not been our goal. In some of the theories, our exposition offers a selection of important, representative theorems, some other cases are treated more systematically. As in the first book, we treat only approximation of functions of one real variable. Thus, functions of several variables, complex approximation or interpolation are not treated, although complex variable methods appear often.

Advanced Problems In Constructive Approximation

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Author : Martin D. Buhmann
language : en
Publisher: Birkhäuser
Release Date : 2012-12-08

Advanced Problems In Constructive Approximation written by Martin D. Buhmann and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-08 with Mathematics categories.

The current form of modern approximation theory is shaped by many new de velopments which are the subject of this series of conferences. The International Meetings on Approximation Theory attempt to keep track in particular of fun damental advances in the theory of function approximation, for example by (or thogonal) polynomials, (weighted) interpolation, multivariate quasi-interpolation, splines, radial basis functions and several others. This includes both approxima tion order and error estimates, as well as constructions of function systems for approximation of functions on Euclidean spaces and spheres. It is a piece of very good fortune that at all of the IDoMAT meetings, col leagues and friends from all over Europe, and indeed some count ries outside Europe and as far away as China, New Zealand, South Africa and U.S.A. came and dis cussed mathematics at IDoMAT conference facility in Witten-Bommerholz. The conference was, as always, held in a friendly and congenial atmosphere. After each meeting, the delegat es were invited to contribute to the proceed ing's volume, the previous one being published in the same Birkhäuser series as this one. The editors were pleased about the quality of the contributions which could be solicited for the book. They are refereed and we should mention our gratitude to the referees and their work.

Mathematics From Leningrad To Austin Volume 2

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Author : Rudolph A. Lorentz
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-07-15

Mathematics From Leningrad To Austin Volume 2 written by Rudolph A. Lorentz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-07-15 with Mathematics categories.

The works of George G. Lorentz, spanning more than 60 years, have played a significant role in the development and evolution of mathematical analysis. The papers presented in this volume represent a selection of his best works, along with commentary from his students and colleagues.

Free Boundary Problems

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Author : Pierluigi Colli
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Free Boundary Problems written by Pierluigi Colli and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Many phenomena of interest for applications are represented by differential equations which are defined in a domain whose boundary is a priori unknown, and is accordingly named a "free boundary". A further quantitative condition is then provided in order to exclude indeterminacy. Free boundary problems thus encompass a broad spectrum which is represented in this state-of-the-art volume by a variety of contributions of researchers in mathematics and applied fields like physics, biology and material sciences. Special emphasis has been reserved for mathematical modelling and for the formulation of new problems.

Nonlinear Smoothing And Multiresolution Analysis

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Author : Carl Rohwer
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-06-16

Nonlinear Smoothing And Multiresolution Analysis written by Carl Rohwer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-16 with Mathematics categories.

This monograph presents a new theory for analysis, comparison and design of nonlinear smoothers, linking to established practices. Although a part of mathematical morphology, the special properties yield many simple, powerful and illuminating results leading to a novel nonlinear multiresolution analysis with pulses that may be as natural to vision as wavelet analysis is to acoustics. Similar to median transforms, they have the advantages of a supporting theory, computational simplicity, remarkable consistency, full trend preservation, and a Parceval-type identity. Although the perspective is new and unfamiliar to most, the reader can verify all the ideas and results with simple simulations on a computer at each stage. The framework developed turns out to be a part of mathematical morphology, but the additional specific structures and properties yield a heuristic understanding that is easy to absorb for practitioners in the fields like signal- and image processing. The book targets mathematicians, scientists and engineers with interest in concepts like trend, pulse, smoothness and resolution in sequences.

Domain Decomposition Methods In Optimal Control Of Partial Differential Equations

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Author : John E. Lagnese
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Domain Decomposition Methods In Optimal Control Of Partial Differential Equations written by John E. Lagnese and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This monograph considers problems of optimal control for partial differential equa tions of elliptic and, more importantly, of hyperbolic types on networked domains. The main goal is to describe, develop and analyze iterative space and time domain decompositions of such problems on the infinite-dimensional level. While domain decomposition methods have a long history dating back well over one hundred years, it is only during the last decade that they have become a major tool in numerical analysis of partial differential equations. A keyword in this context is parallelism. This development is perhaps best illustrated by the fact that we just encountered the 15th annual conference precisely on this topic. Without attempting to provide a complete list of introductory references let us just mention the monograph by Quarteroni and Valli [91] as a general up-to-date reference on domain decomposition methods for partial differential equations. The emphasis of this monograph is to put domain decomposition methods in the context of so-called virtual optimal control problems and, more importantly, to treat optimal control problems for partial differential equations and their decom positions by an all-at-once approach. This means that we are mainly interested in decomposition techniques which can be interpreted as virtual optimal control problems and which, together with the real control problem coming from an un derlying application, lead to a sequence of individual optimal control problems on the subdomains that are iteratively decoupled across the interfaces.

Quasi Interpolation

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Author : Martin Dietrich Buhmann
language : en
Publisher: Cambridge University Press
Release Date : 2022-03-03

Quasi Interpolation written by Martin Dietrich Buhmann and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-03 with Computers categories.

Delve into an in-depth description and analysis of quasi-interpolation, starting from various areas of approximation theory.

Combinatorial And Additive Number Theory Vi

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Author : Melvyn B. Nathanson
language : en
Publisher: Springer Nature
Release Date : 2025-02-21

Combinatorial And Additive Number Theory Vi written by Melvyn B. Nathanson and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-21 with Mathematics categories.

This proceedings volume, the sixth in a series from the Combinatorial and Additive Number Theory (CANT) conferences, is based on talks from the 20th and 21st annual workshops, held in New York in 2022 (virtual) and 2023 (hybrid) respectively. Organized every year since 2003 by the New York Number Theory Seminar at the CUNY Graduate Center, the workshops survey state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics. In this volume, the reader will find peer-reviewed and edited papers on current topics in number theory. This selection of articles will be of relevance to both researchers and graduate students interested in current progress in number theory.

The Random Cluster Model

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Author : Geoffrey R. Grimmett
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-12-13

The Random Cluster Model written by Geoffrey R. Grimmett and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-13 with Mathematics categories.

The random-cluster model has emerged as a key tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is a mix of arguments from probability and geometry. The Random-Cluster Model contains accounts of the subcritical and supercritical phases, together with clear statements of important open problems. The book includes treatment of the first-order (discontinuous) phase transition.