Approximation Theory and Approximation Practice

Author: Lloyd N. Trefethen

Publisher: SIAM

ISBN: 9781611972405

Category: Mathematics

Page: 295

View: 9260

An original and modern treatment of approximation theory for students in applied mathematics. Includes exercises, illustrations and Matlab code.

Journal of Approximation Theory and Applied Mathematics - 2015

Author: Marco Schuchmann

Publisher: BoD – Books on Demand

ISBN: 3741255300

Category: Mathematics

Page: 64

View: 8305

Journal of Approximation Theory and Applied Mathematics (ISSN 2196-1581) is a journal which started in 2013. Themes of our journal are: Approximation theory (with a focus on wavelets) and applications in mathematics like numerical analysis, statistics or financial mathematics.

Chebyshev Polynomials

From Approximation Theory to Algebra and Number Theory

Author: Theodore J. Rivlin

Publisher: Wiley-Interscience


Category: Mathematics

Page: 249

View: 8154

This Secodnd Edition continues the fine tradition of its predecessor by surveying the most important properties of the Chebyshev polynomials and introducing mathematical analysis. New to this edition are approximately 80 exercises and a chapter which introduces some elementary algebraic and number theoretic properties of the Chebyshev polynomials. Additional coverage focuses on extremal and iterative properties.

Kernel-based Approximation Methods using MATLAB

Author: Gregory Fasshauer,Michael McCourt

Publisher: World Scientific Publishing Company

ISBN: 9814630152

Category: Mathematics

Page: 536

View: 3595

In an attempt to introduce application scientists and graduate students to the exciting topic of positive definite kernels and radial basis functions, this book presents modern theoretical results on kernel-based approximation methods and demonstrates their implementation in various settings. The authors explore the historical context of this fascinating topic and explain recent advances as strategies to address long-standing problems. Examples are drawn from fields as diverse as function approximation, spatial statistics, boundary value problems, machine learning, surrogate modeling and finance. Researchers from those and other fields can recreate the results within using the documented MATLAB code, also available through the online library. This combination of a strong theoretical foundation and accessible experimentation empowers readers to use positive definite kernels on their own problems of interest.

Wissenschaftliches Rechnen mit MATLAB

Author: Alfio Quarteroni,Fausto Saleri

Publisher: Springer-Verlag

ISBN: 3540293078

Category: Mathematics

Page: 269

View: 5764

Aus den Rezensionen der englischen Auflage: Dieses Lehrbuch ist eine Einführung in das Wissenschaftliche Rechnen und diskutiert Algorithmen und deren mathematischen Hintergrund. Angesprochen werden im Detail nichtlineare Gleichungen, Approximationsverfahren, numerische Integration und Differentiation, numerische Lineare Algebra, gewöhnliche Differentialgleichungen und Randwertprobleme. Zu den einzelnen Themen werden viele Beispiele und Übungsaufgaben sowie deren Lösung präsentiert, die durchweg in MATLAB formuliert sind. Der Leser findet daher nicht nur die graue Theorie sondern auch deren Umsetzung in numerischen, in MATLAB formulierten Code. MATLAB select 2003, Issue 2, p. 50. [Die Autoren] haben ein ausgezeichnetes Werk vorgelegt, das MATLAB vorstellt und eine sehr nützliche Sammlung von MATLAB Funktionen für die Lösung fortgeschrittener mathematischer und naturwissenschaftlicher Probleme bietet. [...] Die Präsentation des Stoffs ist durchgängig gut und leicht verständlich und beinhaltet Lösungen für die Übungen am Ende jedes Kapitels. Als exzellenter Neuzugang für Universitätsbibliotheken- und Buchhandlungen wird dieses Buch sowohl beim Selbststudium als auch als Ergänzung zu anderen MATLAB-basierten Büchern von großem Nutzen sein. Alles in allem: Sehr empfehlenswert. Für Studenten im Erstsemester wie für Experten gleichermassen. S.T. Karris, University of California, Berkeley, Choice 2003.

Practical Applied Mathematics

Modelling, Analysis, Approximation

Author: Sam Howison

Publisher: Cambridge University Press

ISBN: 9780521842747

Category: Mathematics

Page: 326

View: 1610

This book illustrates how the reader's knowledge of applied mathematics can be used to describe the world around them.

Reelle und Komplexe Analysis

Author: Walter Rudin

Publisher: Walter de Gruyter

ISBN: 9783486591866

Category: Analysis - Lehrbuch

Page: 499

View: 787

Besonderen Wert legt Rudin darauf, dem Leser die Zusammenhänge unterschiedlicher Bereiche der Analysis zu vermitteln und so die Grundlage für ein umfassenderes Verständnis zu schaffen. Das Werk zeichnet sich durch seine wissenschaftliche Prägnanz und Genauigkeit aus und hat damit die Entwicklung der modernen Analysis in nachhaltiger Art und Weise beeinflusst. Der "Baby-Rudin" gehört weltweit zu den beliebtesten Lehrbüchern der Analysis und ist in 13 Sprachen übersetzt. 1993 wurde es mit dem renommierten Steele Prize for Mathematical Exposition der American Mathematical Society ausgezeichnet. Übersetzt von Uwe Krieg.

Mathematics for Industry

Challenges and Frontiers. A Process View: Practice and Theory

Author: David R. Ferguson,Thomas J. Peters,Society for Industrial and Applied Mathematics

Publisher: SIAM

ISBN: 9780898715989

Category: Mathematics

Page: 249

View: 6714

The papers were elicited primarily from Mathematics for Industry: Challenges and Frontiers, a conference sponsored by SIAM in October, 2003.

E.B. Christoffel

The Influence of His Work on Mathematics and the Physical Sciences


Publisher: Springer-Verlag

ISBN: 3034854528

Category: Science

Page: 761

View: 8350

Approximation and Modeling with B-Splines

Author: Klaus HoÓllig,JÓorg HÓorner

Publisher: SIAM

ISBN: 1611972949

Category: Mathematics

Page: 214

View: 6271

B-splines are fundamental to approximation and data fitting, geometric modeling, automated manufacturing, computer graphics, and numerical simulation. With an emphasis on key results and methods that are most widely used in practice, this textbook provides a unified introduction to the basic components of B-spline theory: approximation methods (mathematics), modeling techniques (engineering), and geometric algorithms (computer science). A supplemental Web site will provide a collection of problems, some with solutions, slides for use in lectures, and programs with demos.

Mathematical Tools for Physicists

Author: Michael Grinfeld

Publisher: John Wiley & Sons

ISBN: 3527684271

Category: Science

Page: 632

View: 6688

The new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.

Practical Extrapolation Methods

Theory and Applications

Author: Avram Sidi

Publisher: Cambridge University Press

ISBN: 9780521661591

Category: Computers

Page: 519

View: 3922

This book is concerned with the coherent treatment, including the derivation, analysis, and applications, of the most useful scalar extrapolation methods. Its importance is rooted in the fact that the methods it discusses are geared towards problems that arise commonly in scientific and engineering disciplines. It differs from existing books on the subject in that it concentrates on the most powerful nonlinear methods, presents in-depth treatments of them, and shows which methods are most effective for different classes of practical nontrivial problems, and also shows how to apply these methods to obtain best results.

Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques

11th International Workshop, APPROX 2008 and 12th International Workshop, RANDOM 2008, Boston, MA, USA, August 25-27, 2008

Author: Ashish Goel,Klaus Jansen,José Rolim,Ronitt Rubinfeld

Publisher: Springer Science & Business Media

ISBN: 3540853626

Category: Computers

Page: 604

View: 924

This book constitutes the joint refereed proceedings of the 11th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2008 and the 12th International Workshop on Randomization and Computation, RANDOM 2008, held in Boston, MA, USA, in August 2008. The 20 revised full papers of the APPROX 2008 workshop were carefully reviewed and selected from 42 submissions and focus on algorithmic and complexity issues surrounding the development of efficient approximate solutions to computationally difficult problems. RANDOM 2008 is concerned with applications of randomness to computational and combinatorial problems and accounts for 27 revised full papers, also diligently reviewed and selected out of 52 workshop submissions.


Eulers Konstante, Primzahlstrände und die Riemannsche Vermutung

Author: Julian Havil

Publisher: Springer-Verlag

ISBN: 3540484965

Category: Mathematics

Page: 302

View: 8979

Jeder kennt p = 3,14159..., viele kennen e = 2,71828..., einige i. Und dann? Die "viertwichtigste" Konstante ist die Eulersche Zahl g = 0,5772156... - benannt nach dem genialen Leonhard Euler (1707-1783). Bis heute ist unbekannt, ob g eine rationale Zahl ist. Das Buch lotet die "obskure" Konstante aus. Die Reise beginnt mit Logarithmen und der harmonischen Reihe. Es folgen Zeta-Funktionen und Eulers wunderbare Identität, Bernoulli-Zahlen, Madelungsche Konstanten, Fettfinger in Wörterbüchern, elende mathematische Würmer und Jeeps in der Wüste. Besser kann man nicht über Mathematik schreiben. Was Julian Havil dazu zu sagen hat, ist spektakulär.

Theory and Practice of Finite Elements

Author: Alexandre Ern,Jean-Luc Guermond

Publisher: Springer Science & Business Media

ISBN: 1475743556

Category: Mathematics

Page: 526

View: 5581

This text presenting the mathematical theory of finite elements is organized into three main sections. The first part develops the theoretical basis for the finite element methods, emphasizing inf-sup conditions over the more conventional Lax-Milgrim paradigm. The second and third parts address various applications and practical implementations of the method, respectively. It contains numerous examples and exercises.

A Course on Rough Paths

With an Introduction to Regularity Structures

Author: Peter K. Friz,Martin Hairer

Publisher: N.A

ISBN: 9783319083339


Page: 268

View: 1996

Semantics II: Interpretation and Truth

Semantics II: Interpretation and Truth

Author: Mario BUNGE

Publisher: Springer Science & Business Media

ISBN: 9789027705358

Category: Science

Page: 212

View: 1734

Green's Functions and Boundary Value Problems

Author: Ivar Stakgold,Michael J. Holst

Publisher: John Wiley & Sons

ISBN: 0470906529

Category: Mathematics

Page: 736

View: 5241

Praise for the Second Edition "This book is an excellent introduction to the wide field of boundary value problems."—Journal of Engineering Mathematics "No doubt this textbook will be useful for both students and research workers."—Mathematical Reviews A new edition of the highly-acclaimed guide to boundary value problems, now featuring modern computational methods and approximation theory Green's Functions and Boundary Value Problems, Third Edition continues the tradition of the two prior editions by providing mathematical techniques for the use of differential and integral equations to tackle important problems in applied mathematics, the physical sciences, and engineering. This new edition presents mathematical concepts and quantitative tools that are essential for effective use of modern computational methods that play a key role in the practical solution of boundary value problems. With a careful blend of theory and applications, the authors successfully bridge the gap between real analysis, functional analysis, nonlinear analysis, nonlinear partial differential equations, integral equations, approximation theory, and numerical analysis to provide a comprehensive foundation for understanding and analyzing core mathematical and computational modeling problems. Thoroughly updated and revised to reflect recent developments, the book includes an extensive new chapter on the modern tools of computational mathematics for boundary value problems. The Third Edition features numerous new topics, including: Nonlinear analysis tools for Banach spaces Finite element and related discretizations Best and near-best approximation in Banach spaces Iterative methods for discretized equations Overview of Sobolev and Besov space linear Methods for nonlinear equations Applications to nonlinear elliptic equations In addition, various topics have been substantially expanded, and new material on weak derivatives and Sobolev spaces, the Hahn-Banach theorem, reflexive Banach spaces, the Banach Schauder and Banach-Steinhaus theorems, and the Lax-Milgram theorem has been incorporated into the book. New and revised exercises found throughout allow readers to develop their own problem-solving skills, and the updated bibliographies in each chapter provide an extensive resource for new and emerging research and applications. With its careful balance of mathematics and meaningful applications, Green's Functions and Boundary Value Problems, Third Edition is an excellent book for courses on applied analysis and boundary value problems in partial differential equations at the graduate level. It is also a valuable reference for mathematicians, physicists, engineers, and scientists who use applied mathematics in their everyday work.