Interpolating Cubic Splines
Interpolating Cubic Splines

Author: Gary D. Knott

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 247

ISBN-13: 1461213207

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A spline is a thin flexible strip composed of a material such as bamboo or steel that can be bent to pass through or near given points in the plane, or in 3-space in a smooth manner. Mechanical engineers and drafting specialists find such (physical) splines useful in designing and in drawing plans for a wide variety of objects, such as for hulls of boats or for the bodies of automobiles where smooth curves need to be specified. These days, physi cal splines are largely replaced by computer software that can compute the desired curves (with appropriate encouragment). The same mathematical ideas used for computing "spline" curves can be extended to allow us to compute "spline" surfaces. The application ofthese mathematical ideas is rather widespread. Spline functions are central to computer graphics disciplines. Spline curves and surfaces are used in computer graphics renderings for both real and imagi nary objects. Computer-aided-design (CAD) systems depend on algorithms for computing spline functions, and splines are used in numerical analysis and statistics. Thus the construction of movies and computer games trav els side-by-side with the art of automobile design, sail construction, and architecture; and statisticians and applied mathematicians use splines as everyday computational tools, often divorced from graphic images.

The Theory of Splines and Their Applications
The Theory of Splines and Their Applications

Author: J. H. Ahlberg

Publisher: Elsevier

Published: 2016-06-03

Total Pages: 297

ISBN-13: 1483222950

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The Theory of Splines and Their Applications discusses spline theory, the theory of cubic splines, polynomial splines of higher degree, generalized splines, doubly cubic splines, and two-dimensional generalized splines. The book explains the equations of the spline, procedures for applications of the spline, convergence properties, equal-interval splines, and special formulas for numerical differentiation or integration. The text explores the intrinsic properties of cubic splines including the Hilbert space interpretation, transformations defined by a mesh, and some connections with space technology concerning the payload of a rocket. The book also discusses the theory of polynomial splines of odd degree which can be approached through algebraically (which depends primarily on the examination in detail of the linear system of equations defining the spline). The theory can also be approached intrinsically (which exploits the consequences of basic integral relations existing between functions and approximating spline functions). The text also considers the second integral relation, raising the order of convergence, and the limits on the order of convergence. The book will prove useful for mathematicians, physicist, engineers, or academicians in the field of technology and applied mathematics.

Local Polynomial Modelling and Its Applications
Local Polynomial Modelling and Its Applications

Author: Jianqing Fan

Publisher: CRC Press

Published: 1996-03-01

Total Pages: 362

ISBN-13: 9780412983214

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Data-analytic approaches to regression problems, arising from many scientific disciplines are described in this book. The aim of these nonparametric methods is to relax assumptions on the form of a regression function and to let data search for a suitable function that describes the data well. The use of these nonparametric functions with parametric techniques can yield very powerful data analysis tools. Local polynomial modeling and its applications provides an up-to-date picture on state-of-the-art nonparametric regression techniques. The emphasis of the book is on methodologies rather than on theory, with a particular focus on applications of nonparametric techniques to various statistical problems. High-dimensional data-analytic tools are presented, and the book includes a variety of examples. This will be a valuable reference for research and applied statisticians, and will serve as a textbook for graduate students and others interested in nonparametric regression.

Object-Oriented Implementation of Numerical Methods
Object-Oriented Implementation of Numerical Methods

Author: Didier H. Besset

Publisher: Morgan Kaufmann

Published: 2001

Total Pages: 800

ISBN-13: 9781558606791

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"There are few books that show how to build programs of any kind. One common theme is compiler building, and there are shelves full of them. There are few others. It's an area, or a void, that needs filling. this book does a great job of showing how to build numerical analysis programs." -David N. Smith, IBM T J Watson Research Center Numerical methods naturally lend themselves to an object-oriented approach. Mathematics builds high- level ideas on top of previously described, simpler ones. Once a property is demonstrated for a given concept, it can be applied to any new concept sharing the same premise as the original one, similar to the ideas of reuse and inheritance in object-oriented (OO) methodology. Few books on numerical methods teach developers much about designing and building good code. Good computing routines are problem-specific. Insight and understanding are what is needed, rather than just recipes and black box routines. Developers need the ability to construct new programs for different applications. Object-Oriented Implementation of Numerical Methods reveals a complete OO design methodology in a clear and systematic way. Each method is presented in a consistent format, beginning with a short explanation and following with a description of the general OO architecture for the algorithm. Next, the code implementations are discussed and presented along with real-world examples that the author, an experienced software engineer, has used in a variety of commercial applications. Features: Reveals the design methodology behind the code, including design patterns where appropriate, rather than just presenting canned solutions. Implements all methods side by side in both Java and Smalltalk. This contrast can significantly enhance your understanding of the nature of OO programming languages. Provides a step-by-step pathway to new object-oriented techniques for programmers familiar with using procedural languages such as C or Fortran for numerical methods. Includes a chapter on data mining, a key application of numerical methods.

Advances in Visual Computing
Advances in Visual Computing

Author: George Bebis

Publisher: Springer Science & Business Media

Published: 2009-11-17

Total Pages: 1238

ISBN-13: 364210519X

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The two volume set LNCS 5875 and LNCS 5876 constitutes the refereed proceedings of the 5th International Symposium on Visual Computing, ISVC 2009, held in Las Vegas, NV, USA, in November/December 2009. The 97 revised full papers and 63 poster papers presented together with 40 full and 15 poster papers of 7 special tracks were carefully reviewed and selected from more than 320 submissions. The papers are organized in topical sections on computer graphics; visualization; feature extraction and matching; medical imaging; motion; virtual reality; face processing; reconstruction; detection and tracking; applications; and video analysis and event recognition. The 7 additional special tracks address issues such as object recognition; visual computing for robotics; computational bioimaging; 3D mapping, modeling and surface reconstruction; deformable models: theory and applications; visualization enhanced data analysis for health applications; and optimization for vision, graphics and medical imaging: theory and applications.

Wavelets and Filter Banks
Wavelets and Filter Banks

Author: Gilbert Strang

Publisher: SIAM

Published: 1996-10-01

Total Pages: 556

ISBN-13: 9780961408879

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A comprehensive treatment of wavelets for both engineers and mathematicians.

Robotic Systems
Robotic Systems

Author: S.G. Tzafestas

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 625

ISBN-13: 9401125260

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Robotics is a modern interdisciplinary field that has emerged from the marriage of computerized numerical control and remote manipulation. Today's robotic systems have intelligence features, and are able to perform dexterous and intelligent human-like actions through appropriate combination of learning, perception, planning, decision making and control. This book presents advanced concepts, techniques and applications reflecting the experience of a wide group of specialists in the field. Topics include: kinematics, dynamics, path planning and tracking, control, mobile robotics, navigation, robot programming, and sophisticated applications in the manufacturing, medical, and other areas.

Computer Aided Analysis and Design
Computer Aided Analysis and Design

Author: Srinivasa Prakash Regalla

Publisher: I. K. International Pvt Ltd

Published: 2013-12-30

Total Pages: 279

ISBN-13: 9380026455

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The book has all the details required for the complete coverage of either undergraduate level or graduate level course on Computer Aided Design for mechanical engineers, design engineers and civil and architectural engineers. Emphasis has been laid on explaining the concepts and techniques more from the practical and implementation standpoint so that the reader can begin hands-on and to enable the reader to write his own programs and design CAD systems for any mechanical element. Each chapter has a large number of solved and unsolved exercise problems. The book is complemented by several open ended projects, topics as well as partial details of solution, in all the chapters. Close knitting among the geometric modeling, computer aided engineering and applications such as rapid prototyping is a special feature of this book. Spread in two parts containing 11 chapters the book broadly covers: " Background of the CAD systems. " Curve, surface and solid modeling techniques " Rapid prototyping technology. " Fundamental techniques of computer aided engineering " Fundamentals of mechanical systems " Numerical techniques for analysis of mechanical systems " Finite difference method and finite element method.

Semiparametric Regression for the Social Sciences
Semiparametric Regression for the Social Sciences

Author: Luke John Keele

Publisher: John Wiley & Sons

Published: 2008-04-15

Total Pages: 230

ISBN-13: 9780470998120

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An introductory guide to smoothing techniques, semiparametric estimators, and their related methods, this book describes the methodology via a selection of carefully explained examples and data sets. It also demonstrates the potential of these techniques using detailed empirical examples drawn from the social and political sciences. Each chapter includes exercises and examples and there is a supplementary website containing all the datasets used, as well as computer code, allowing readers to replicate every analysis reported in the book. Includes software for implementing the methods in S-Plus and R.

An Introduction to Numerical Analysis
An Introduction to Numerical Analysis

Author: Endre Süli

Publisher: Cambridge University Press

Published: 2003-08-28

Total Pages: 440

ISBN-13: 9780521007948

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An introduction to numerical analysis combining rigour with practical applications, and providing numerous exercises plus solutions.