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Stable Approximate Evaluation of Unbounded Operators

Stable Approximate Evaluation of Unbounded Operators PDF Author: C. W. Groetsch
Publisher: Springer Science & Business Media
ISBN: 3540399429
Category : Mathematics
Languages : en
Pages : 134

Book Description
Spectral theory of bounded linear operators teams up with von Neumann’s theory of unbounded operators in this monograph to provide a general framework for the study of stable methods for the evaluation of unbounded operators. An introductory chapter provides numerous illustrations of unbounded linear operators that arise in various inverse problems of mathematical physics. Before the general theory of stabilization methods is developed, an extensive exposition of the necessary background material from the theory of operators on Hilbert space is provided. Several specific stabilization methods are studied in detail, with particular attention to the Tikhonov-Morozov method and its iterated version.

Stable Approximate Evaluation of Unbounded Operators

Stable Approximate Evaluation of Unbounded Operators PDF Author: C. W. Groetsch
Publisher: Springer Science & Business Media
ISBN: 3540399429
Category : Mathematics
Languages : en
Pages : 134

Book Description
Spectral theory of bounded linear operators teams up with von Neumann’s theory of unbounded operators in this monograph to provide a general framework for the study of stable methods for the evaluation of unbounded operators. An introductory chapter provides numerous illustrations of unbounded linear operators that arise in various inverse problems of mathematical physics. Before the general theory of stabilization methods is developed, an extensive exposition of the necessary background material from the theory of operators on Hilbert space is provided. Several specific stabilization methods are studied in detail, with particular attention to the Tikhonov-Morozov method and its iterated version.

Stable Approximate Evaluation of Unbounded Operators

Stable Approximate Evaluation of Unbounded Operators PDF Author: Charles W. Groetsch
Publisher:
ISBN:
Category : Approximation theory
Languages : en
Pages : 0

Book Description


Random Perturbation of PDEs and Fluid Dynamic Models

Random Perturbation of PDEs and Fluid Dynamic Models PDF Author: Franco Flandoli
Publisher: Springer
ISBN: 3642182313
Category : Mathematics
Languages : en
Pages : 187

Book Description
The book deals with the random perturbation of PDEs which lack well-posedness, mainly because of their non-uniqueness, in some cases because of blow-up. The aim is to show that noise may restore uniqueness or prevent blow-up. This is not a general or easy-to-apply rule, and the theory presented in the book is in fact a series of examples with a few unifying ideas. The role of additive and bilinear multiplicative noise is described and a variety of examples are included, from abstract parabolic evolution equations with non-Lipschitz nonlinearities to particular fluid dynamic models, like the dyadic model, linear transport equations and motion of point vortices.

Computational Approach to Riemann Surfaces

Computational Approach to Riemann Surfaces PDF Author: Alexander I. Bobenko
Publisher: Springer Science & Business Media
ISBN: 3642174124
Category : Mathematics
Languages : en
Pages : 268

Book Description
This volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically available numerical codes in this field. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surface theory are presented. The intended audience of this book is twofold. It can be used as a textbook for a graduate course in numerics of Riemann surfaces, in which case the standard undergraduate background, i.e., calculus and linear algebra, is required. In particular, no knowledge of the theory of Riemann surfaces is expected; the necessary background in this theory is contained in the Introduction chapter. At the same time, this book is also intended for specialists in geometry and mathematical physics applying the theory of Riemann surfaces in their research. It is the first book on numerics of Riemann surfaces that reflects the progress made in this field during the last decade, and it contains original results. There are a growing number of applications that involve the evaluation of concrete characteristics of models analytically described in terms of Riemann surfaces. Many problem settings and computations in this volume are motivated by such concrete applications in geometry and mathematical physics.

Fatou, Julia, Montel

Fatou, Julia, Montel PDF Author: Michèle Audin
Publisher: Springer
ISBN: 3642178545
Category : Mathematics
Languages : en
Pages : 342

Book Description
How did Pierre Fatou and Gaston Julia create what we now call Complex Dynamics, in the context of the early twentieth century and especially of the First World War? The book is based partly on new, unpublished sources. Who were Pierre Fatou, Gaston Julia, Paul Montel? New biographical information is given on the little known mathematician that was Pierre Fatou. How did the WW1 injury of Julia influence mathematical life in France? From the reviews of the French version: "Audin’s book is ... filled with marvelous biographical information and analysis, dealing not just with the men mentioned in the book’s title but a large number of other players, too ... [It] addresses itself to scholars for whom the history of mathematics has a particular resonance and especially to mathematicians active, or even with merely an interest, in complex dynamics. ... presents it all to the reader in a very appealing form." (Michael Berg, The Mathematical Association of America, October 2009)

Some Mathematical Models from Population Genetics

Some Mathematical Models from Population Genetics PDF Author: Alison Etheridge
Publisher: Springer
ISBN: 3642166326
Category : Mathematics
Languages : en
Pages : 129

Book Description
This work reflects sixteen hours of lectures delivered by the author at the 2009 St Flour summer school in probability. It provides a rapid introduction to a range of mathematical models that have their origins in theoretical population genetics. The models fall into two classes: forwards in time models for the evolution of frequencies of different genetic types in a population; and backwards in time (coalescent) models that trace out the genealogical relationships between individuals in a sample from the population. Some, like the classical Wright-Fisher model, date right back to the origins of the subject. Others, like the multiple merger coalescents or the spatial Lambda-Fleming-Viot process are much more recent. All share a rich mathematical structure. Biological terms are explained, the models are carefully motivated and tools for their study are presented systematically.

Affine Density in Wavelet Analysis

Affine Density in Wavelet Analysis PDF Author: Gitta Kutyniok
Publisher: Springer Science & Business Media
ISBN: 3540729496
Category : Mathematics
Languages : en
Pages : 149

Book Description
This volume provides a thorough and comprehensive treatment of irregular wavelet frames. It introduces and employs a new notion of affine density as a highly effective tool for examining the geometry of sequences of time-scale indices. Coverage includes non-existence of irregular co-affine frames, the Nyquist phenomenon for wavelet systems, and approximation properties of irregular wavelet frames.

Spin Glasses

Spin Glasses PDF Author: Erwin Bolthausen
Publisher: Springer
ISBN: 3540409084
Category : Science
Languages : en
Pages : 190

Book Description
This book serves as a concise introduction to the state-of-the-art of spin glass theory. The collection of review papers are written by leading experts in the field and cover the topic from a wide variety of angles. The book will be useful to both graduate students and young researchers, as well as to anyone curious to know what is going on in this exciting area of mathematical physics.

Iterative Regularization Methods for Nonlinear Ill-Posed Problems

Iterative Regularization Methods for Nonlinear Ill-Posed Problems PDF Author: Barbara Kaltenbacher
Publisher: Walter de Gruyter
ISBN: 311020827X
Category : Mathematics
Languages : en
Pages : 205

Book Description
Nonlinear inverse problems appear in many applications, and typically they lead to mathematical models that are ill-posed, i.e., they are unstable under data perturbations. Those problems require a regularization, i.e., a special numerical treatment. This book presents regularization schemes which are based on iteration methods, e.g., nonlinear Landweber iteration, level set methods, multilevel methods and Newton type methods.

Calculus of Variations and Nonlinear Partial Differential Equations

Calculus of Variations and Nonlinear Partial Differential Equations PDF Author: Luigi Ambrosio
Publisher: Springer Science & Business Media
ISBN: 3540759131
Category : Mathematics
Languages : en
Pages : 213

Book Description
With a historical overview by Elvira Mascolo