Essays on the Complexity of Continuous Problems
Essays on the Complexity of Continuous Problems

Author: Erich Novak

Publisher: European Mathematical Society

Published: 2009

Total Pages: 112

ISBN-13: 9783037190692

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This book contains five essays on the complexity of continuous problems, written for a wider audience. The first four essays are based on talks presented in 2008 when Henryk Wozniakowski received an honorary doctoral degree from the Friedrich Schiller University of Jena. The focus is on the introduction and history of the complexity of continuous problems, as well as on recent progress concerning the complexity of high-dimensional numerical problems. The last essay provides a brief and informal introduction to the basic notions and concepts of information-based complexity addressed to a general readership.

Tractability of Multivariate Problems: Standard information for functionals
Tractability of Multivariate Problems: Standard information for functionals

Author: Erich Novak

Publisher: European Mathematical Society

Published: 2008

Total Pages: 684

ISBN-13: 9783037190845

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This is the second volume of a three-volume set comprising a comprehensive study of the tractability of multivariate problems. The second volume deals with algorithms using standard information consisting of function values for the approximation of linear and selected nonlinear functionals. An important example is numerical multivariate integration. The proof techniques used in volumes I and II are quite different. It is especially hard to establish meaningful lower error bounds for the approximation of functionals by using finitely many function values. Here, the concept of decomposable reproducing kernels is helpful, allowing it to find matching lower and upper error bounds for some linear functionals. It is then possible to conclude tractability results from such error bounds. Tractability results, even for linear functionals, are very rich in variety. There are infinite-dimensional Hilbert spaces for which the approximation with an arbitrarily small error of all linear functionals requires only one function value. There are Hilbert spaces for which all nontrivial linear functionals suffer from the curse of dimensionality. This holds for unweighted spaces, where the role of all variables and groups of variables is the same. For weighted spaces one can monitor the role of all variables and groups of variables. Necessary and sufficient conditions on the decay of the weights are given to obtain various notions of tractability. The text contains extensive chapters on discrepancy and integration, decomposable kernels and lower bounds, the Smolyak/sparse grid algorithms, lattice rules and the CBC (component-by-component) algorithms. This is done in various settings. Path integration and quantum computation are also discussed. This volume is of interest to researchers working in computational mathematics, especially in approximation of high-dimensional problems. It is also well suited for graduate courses and seminars. There are 61 open problems listed to stimulate future research in tractability.

The Human Face Of Computing
The Human Face Of Computing

Author: Cristian S Calude

Publisher: World Scientific

Published: 2015-08-04

Total Pages: 449

ISBN-13: 1783266457

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Computation is ubiquitous: modern life would be inconceivable without it.Written as a series of conversations with influential computer scientists, mathematicians and physicists, this book provides access to the inner thinking of those who have made essential contributions to the development of computing and its applications. You will learn about the interviewees' education, career path, influences, methods of work, how they cope with failure and success, how they relax, how they see the future, and much more.The conversations are presented in jargon-free language suitable for a general audience, but with enough technical detail for more specialized readers. The aim of the book is not only to inform and entertain, but also to motivate and stimulate.

Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan
Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan

Author: Josef Dick

Publisher: Springer

Published: 2018-05-23

Total Pages: 1330

ISBN-13: 3319724568

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This book is a tribute to Professor Ian Hugh Sloan on the occasion of his 80th birthday. It consists of nearly 60 articles written by international leaders in a diverse range of areas in contemporary computational mathematics. These papers highlight the impact and many achievements of Professor Sloan in his distinguished academic career. The book also presents state of the art knowledge in many computational fields such as quasi-Monte Carlo and Monte Carlo methods for multivariate integration, multi-level methods, finite element methods, uncertainty quantification, spherical designs and integration on the sphere, approximation and interpolation of multivariate functions, oscillatory integrals, and in general in information-based complexity and tractability, as well as in a range of other topics. The book also tells the life story of the renowned mathematician, family man, colleague and friend, who has been an inspiration to many of us. The reader may especially enjoy the story from the perspective of his family, his wife, his daughter and son, as well as grandchildren, who share their views of Ian. The clear message of the book is that Ian H. Sloan has been a role model in science and life.

Collection Of Essays On Complexity And Management, A - Proceedings Of The Summer School On Managerial Complexity
Collection Of Essays On Complexity And Management, A - Proceedings Of The Summer School On Managerial Complexity

Author: Walter Baets

Publisher: World Scientific

Published: 1999-04-01

Total Pages: 338

ISBN-13: 9814544108

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A tendency exists in management theory and practice today to accept that our linear and deterministic ways of thinking about managerial problems create more problems than they solve. In the field of strategy studies, for instance, one can observe a growing interest in learning and organisational flexibility — IT gives importance to distributed cognition and adaptive systems. Management theorists are keenly observing developments surrounding complexity and chaos theory in science, and management researchers are attempting to apply emerging theories to managerial problems.Although there are still a limited number of applications in the managerial world, the Santa Fe Institute and the Los Alamos Center for Nonlinear Studies (both in the US) have been active for several years in closely related fields and, more important, adopt a multidisciplinary approach. Such applied research is seldom present in academic management journals. It seems, however, that the business community is interested in the implications of chaos and complexity for management as well as adopting a multidisciplinary approach to strategy and organisational change.This volume, constituting the proceedings of the Summer School on Managerial Complexity, held in Granada, Spain, on 11-25 July 1998, will benefit students and researchers in chaos and dynamical systems.

The Best Writing on Mathematics 2010
The Best Writing on Mathematics 2010

Author: Mircea Pitici

Publisher: Princeton University Press

Published: 2021-09-14

Total Pages: 435

ISBN-13: 1400836123

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The year’s most memorable writing on mathematics This anthology brings together the year's finest writing on mathematics from around the world. Featuring promising new voices alongside some of the foremost names in mathematics, The Best Writing on Mathematics makes available to a wide audience many articles not easily found anywhere else—and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here readers will discover why Freeman Dyson thinks some mathematicians are birds while others are frogs; why Keith Devlin believes there's more to mathematics than proof; what Nick Paumgarten has to say about the timing patterns of New York City's traffic lights (and why jaywalking is the most mathematically efficient way to cross Sixty-sixth Street); what Samuel Arbesman can tell us about the epidemiology of the undead in zombie flicks; and much, much more. In addition to presenting the year's most memorable writing on mathematics, this must-have anthology also includes a foreword by esteemed mathematician William Thurston and an informative introduction by Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where it's headed.

Numerical Analysis
Numerical Analysis

Author: Walter Gautschi

Publisher: Springer Science & Business Media

Published: 2011-12-06

Total Pages: 611

ISBN-13: 0817682597

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Revised and updated, this second edition of Walter Gautschi's successful Numerical Analysis explores computational methods for problems arising in the areas of classical analysis, approximation theory, and ordinary differential equations, among others. Topics included in the book are presented with a view toward stressing basic principles and maintaining simplicity and teachability as far as possible, while subjects requiring a higher level of technicality are referenced in detailed bibliographic notes at the end of each chapter. Readers are thus given the guidance and opportunity to pursue advanced modern topics in more depth. Along with updated references, new biographical notes, and enhanced notational clarity, this second edition includes the expansion of an already large collection of exercises and assignments, both the kind that deal with theoretical and practical aspects of the subject and those requiring machine computation and the use of mathematical software. Perhaps most notably, the edition also comes with a complete solutions manual, carefully developed and polished by the author, which will serve as an exceptionally valuable resource for instructors.

Lattice Rules
Lattice Rules

Author: Josef Dick

Publisher: Springer Nature

Published: 2022-08-24

Total Pages: 584

ISBN-13: 3031099516

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Lattice rules are a powerful and popular form of quasi-Monte Carlo rules based on multidimensional integration lattices. This book provides a comprehensive treatment of the subject with detailed explanations of the basic concepts and the current methods used in research. This comprises, for example, error analysis in reproducing kernel Hilbert spaces, fast component-by-component constructions, the curse of dimensionality and tractability, weighted integration and approximation problems, and applications of lattice rules.

Bases in Function Spaces, Sampling, Discrepancy, Numerical Integration
Bases in Function Spaces, Sampling, Discrepancy, Numerical Integration

Author: Hans Triebel

Publisher: European Mathematical Society

Published: 2010

Total Pages: 314

ISBN-13: 9783037190852

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The first chapters of this book deal with Haar bases, Faber bases and some spline bases for function spaces in Euclidean $n$-space and $n$-cubes. These are used in the subsequent chapters to study sampling and numerical integration preferably in spaces with dominating mixed smoothness. The subject of the last chapter is the symbiotic relationship between numerical integration and discrepancy, measuring the deviation of sets of points from uniformity. This book is addressed to graduate students and mathematicians who have a working knowledge of basic elements of function spaces and approximation theory and who are interested in the subtle interplay between function spaces, complexity theory and number theory (discrepancy).