Lying By Approximation
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| Author | : Vincent C. Prantil |
| Publisher | : Morgan & Claypool Publishers |
| Total Pages | : 116 |
| Release | : 2013-08-01 |
| Genre | : Technology & Engineering |
| ISBN | : 1627052364 |
In teaching an introduction to the finite element method at the undergraduate level, a prudent mix of theory and applications is often sought. In many cases, analysts use the finite element method to perform parametric studies on potential designs to size parts, weed out less desirable design scenarios, and predict system behavior under load. In this book, we discuss common pitfalls encountered by many finite element analysts, in particular, students encountering the method for the first time. We present a variety of simple problems in axial, bending, torsion, and shear loading that combine the students' knowledge of theoretical mechanics, numerical methods, and approximations particular to the finite element method itself. We also present case studies in which analyses are coupled with experiments to emphasize validation, illustrate where interpretations of numerical results can be misleading, and what can be done to allay such tendencies. Challenges in presenting the necessary mix of theory and applications in a typical undergraduate course are discussed. We also discuss a list of tips and rules of thumb for applying the method in practice. Table of Contents: Preface / Acknowledgments / Guilty Until Proven Innocent / Let's Get Started / Where We Begin to Go Wrong / It's Only a Model / Wisdom Is Doing It / Summary / Afterword / Bibliography / Authors' Biographies
| Author | : Vincent Prantil |
| Publisher | : Springer Nature |
| Total Pages | : 94 |
| Release | : 2022-06-01 |
| Genre | : Technology & Engineering |
| ISBN | : 3031793633 |
In teaching an introduction to the finite element method at the undergraduate level, a prudent mix of theory and applications is often sought. In many cases, analysts use the finite element method to perform parametric studies on potential designs to size parts, weed out less desirable design scenarios, and predict system behavior under load. In this book, we discuss common pitfalls encountered by many finite element analysts, in particular, students encountering the method for the first time. We present a variety of simple problems in axial, bending, torsion, and shear loading that combine the students' knowledge of theoretical mechanics, numerical methods, and approximations particular to the finite element method itself. We also present case studies in which analyses are coupled with experiments to emphasize validation, illustrate where interpretations of numerical results can be misleading, and what can be done to allay such tendencies. Challenges in presenting the necessary mix of theory and applications in a typical undergraduate course are discussed. We also discuss a list of tips and rules of thumb for applying the method in practice. Table of Contents: Preface / Acknowledgments / Guilty Until Proven Innocent / Let's Get Started / Where We Begin to Go Wrong / It's Only a Model / Wisdom Is Doing It / Summary / Afterword / Bibliography / Authors' Biographies
| Author | : Patrick Laurie Davies |
| Publisher | : CRC Press |
| Total Pages | : 320 |
| Release | : 2014-07-07 |
| Genre | : Mathematics |
| ISBN | : 148221587X |
The First Detailed Account of Statistical Analysis That Treats Models as ApproximationsThe idea of truth plays a role in both Bayesian and frequentist statistics. The Bayesian concept of coherence is based on the fact that two different models or parameter values cannot both be true. Frequentist statistics is formulated as the problem of estimating
| Author | : Nikolai A. Bobylev |
| Publisher | : Walter de Gruyter |
| Total Pages | : 284 |
| Release | : 2012-05-10 |
| Genre | : Mathematics |
| ISBN | : 3110885719 |
The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Editor-in-Chief Jürgen Appell, Würzburg, Germany Honorary and Advisory Editors Catherine Bandle, Basel, Switzerland Alain Bensoussan, Richardson, Texas, USA Avner Friedman, Columbus, Ohio, USA Umberto Mosco, Worcester, Massachusetts, USA Louis Nirenberg, New York, USA Alfonso Vignoli, Rome, Italy Editorial Board Manuel del Pino, Santiago, Chile Mikio Kato, Nagano, Japan Wojciech Kryszewski, Toruń, Poland Simeon Reich, Haifa, Israel Please submit book proposals to Jürgen Appell. Titles in planning include Eduardo V. Teixeira, Free Boundary Problems: A Primer (2018) Lucio Damascelli and Filomena Pacella, Morse Index of Solutions of Nonlinear Elliptic Equations (2019) Rafael Ortega, Periodic Differential Equations in the Plane: A Topological Perspective (2019) Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020) Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021)
| Author | : Andrei A. Gonchar |
| Publisher | : Springer |
| Total Pages | : 225 |
| Release | : 2008-01-03 |
| Genre | : Mathematics |
| ISBN | : 3540477926 |
The book incorporates research papers and surveys written by participants ofan International Scientific Programme on Approximation Theory jointly supervised by Institute for Constructive Mathematics of University of South Florida at Tampa, USA and the Euler International Mathematical Instituteat St. Petersburg, Russia. The aim of the Programme was to present new developments in Constructive Approximation Theory. The topics of the papers are: asymptotic behaviour of orthogonal polynomials, rational approximation of classical functions, quadrature formulas, theory of n-widths, nonlinear approximation in Hardy algebras,numerical results on best polynomial approximations, wavelet analysis. FROM THE CONTENTS: E.A. Rakhmanov: Strong asymptotics for orthogonal polynomials associated with exponential weights on R.- A.L. Levin, E.B. Saff: Exact Convergence Rates for Best Lp Rational Approximation to the Signum Function and for Optimal Quadrature in Hp.- H. Stahl: Uniform Rational Approximation of x .- M. Rahman, S.K. Suslov: Classical Biorthogonal Rational Functions.- V.P. Havin, A. Presa Sague: Approximation properties of harmonic vector fields and differential forms.- O.G. Parfenov: Extremal problems for Blaschke products and N-widths.- A.J. Carpenter, R.S. Varga: Some Numerical Results on Best Uniform Polynomial Approximation of x on 0,1 .- J.S. Geronimo: Polynomials Orthogonal on the Unit Circle with Random Recurrence Coefficients.- S. Khrushchev: Parameters of orthogonal polynomials.- V.N. Temlyakov: The universality of the Fibonacci cubature formulas.
| Author | : Tatiana Shingel |
| Publisher | : |
| Total Pages | : 100 |
| Release | : 2009 |
| Genre | : Approximation theory |
| ISBN | : |
| Author | : Ding-Zhu Du |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 450 |
| Release | : 2011-11-18 |
| Genre | : Mathematics |
| ISBN | : 1461417015 |
This book is intended to be used as a textbook for graduate students studying theoretical computer science. It can also be used as a reference book for researchers in the area of design and analysis of approximation algorithms. Design and Analysis of Approximation Algorithms is a graduate course in theoretical computer science taught widely in the universities, both in the United States and abroad. There are, however, very few textbooks available for this course. Among those available in the market, most books follow a problem-oriented format; that is, they collected many important combinatorial optimization problems and their approximation algorithms, and organized them based on the types, or applications, of problems, such as geometric-type problems, algebraic-type problems, etc. Such arrangement of materials is perhaps convenient for a researcher to look for the problems and algorithms related to his/her work, but is difficult for a student to capture the ideas underlying the various algorithms. In the new book proposed here, we follow a more structured, technique-oriented presentation. We organize approximation algorithms into different chapters, based on the design techniques for the algorithms, so that the reader can study approximation algorithms of the same nature together. It helps the reader to better understand the design and analysis techniques for approximation algorithms, and also helps the teacher to present the ideas and techniques of approximation algorithms in a more unified way.
| Author | : Michael Golomb |
| Publisher | : |
| Total Pages | : 310 |
| Release | : 1962 |
| Genre | : Approximate computation |
| ISBN | : |
| Author | : Thomas Erlebach |
| Publisher | : Springer |
| Total Pages | : 308 |
| Release | : 2013-12-11 |
| Genre | : Computers |
| ISBN | : 3642380166 |
This book constitutes the thoroughly refereed post workshop proceedings of the 10th International Workshop on Approximation and Online Algorithms, WAOA 2012, held in Ljubljana, Slovenia, in September 2012 as part of the ALGO 2012 conference event. The 22 revised full papers presented together with invited talk were carefully reviewed and selected from 60 submissions. The workshop covered areas such as geometric problems, online algorithms, scheduling, algorithmic game theory, and approximation algorithms.
| Author | : Ashish Goel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 614 |
| Release | : 2008-08-12 |
| Genre | : Computers |
| ISBN | : 3540853626 |
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.
