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Object-Oriented Implementation of Numerical Methods

Author: Didier H. Besset

Publisher: Morgan Kaufmann

Published: 2001

Total Pages: 800

ISBN-13: 9781558606791

"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.

Solving PDEs in C++

Author: Yair Shapira

Publisher: SIAM

Published: 2012-06-07

Total Pages: 775

ISBN-13: 1611972167

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In this much-expanded second edition, author Yair Shapira presents new applications and a substantial extension of the original object-oriented framework to make this popular and comprehensive book even easier to understand and use. It not only introduces the C and C++ programming languages, but also shows how to use them in the numerical solution of partial differential equations (PDEs). The book leads readers through the entire solution process, from the original PDE, through the discretization stage, to the numerical solution of the resulting algebraic system. The high level of abstraction available in C++ is particularly useful in the implementation of complex mathematical objects, such as unstructured mesh, sparse matrix, and multigrid hierarchy, often used in numerical modeling. The well-debugged and tested code segments implement the numerical methods efficiently and transparently in a unified object-oriented approach.

Computing for Numerical Methods Using Visual C++

Author: Shaharuddin Salleh

Publisher: John Wiley & Sons

Published: 2007-12-14

Total Pages: 468

ISBN-13: 0470192623

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A visual, interdisciplinary approach to solving problems in numerical methods Computing for Numerical Methods Using Visual C++ fills the need for a complete, authoritative book on the visual solutions to problems in numerical methods using C++. In an age of boundless research, there is a need for a programming language that can successfully bridge the communication gap between a problem and its computing elements through the use of visual-ization for engineers and members of varying disciplines, such as biologists, medical doctors, mathematicians, economists, and politicians. This book takes an interdisciplinary approach to the subject and demonstrates how solving problems in numerical methods using C++ is dominant and practical for implementation due to its flexible language format, object-oriented methodology, and support for high numerical precisions. In an accessible, easy-to-follow style, the authors cover: Numerical modeling using C++ Fundamental mathematical tools MFC interfaces Curve visualization Systems of linear equations Nonlinear equations Interpolation and approximation Differentiation and integration Eigenvalues and Eigenvectors Ordinary differential equations Partial differential equations This reader-friendly book includes a companion Web site, giving readers free access to all of the codes discussed in the book as well as an equation parser called "MyParser" that can be used to develop various numerical applications on Windows. Computing for Numerical Methods Using Visual C++ serves as an excellent reference for students in upper undergraduate- and graduate-level courses in engineering, science, and mathematics. It is also an ideal resource for practitioners using Microsoft Visual C++.

Solving PDEs in C++

Author: Yair Shapira

Publisher:

Published: 2006

Total Pages: 500

ISBN-13: 9780898718959

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This comprehensive book introduces the C and C++ programming languages and shows how to use them in the numerical solution of partial differential equations (PDEs). It leads the reader through the entire solution process, from the original PDE, through the discretization stage, to the numerical solution of the resulting algebraic system. The well-debugged and tested code segments implement the numerical methods efficiently and transparently. Basic and advanced numerical methods are introduced and implemented easily and efficiently in a unified object-oriented approach. The high level of abstraction available in C++ is particularly useful in the implementation of complex mathematical objects, such as unstructured mesh, sparse matrix, and multigrid hierarchy, often used in numerical modeling. This book introduces a unified approach for the implementation of these objects. Solving PDEs in C++ contains all the required background in programming, PDEs, and numerical methods; only an elementary background in linear algebra and calculus is required. For the more advanced reader, there is also material on stability analysis and weak formulation. The final parts of the book demonstrate the object-oriented approach in advanced applications. Audience: researchers, engineers, and advanced students. It can be used as a textbook in courses in C++ with applications, C++ in engineering, numerical analysis, and numerical PDEs at the advanced undergraduate and graduate levels. Because it is self-contained, the book is also suitable for self-study by researchers and students in applied and computational science and engineering.

Mathematical Objects in C++

Author: Yair Shapira

Publisher: CRC Press

Published: 2009-06-19

Total Pages: 609

ISBN-13: 9781439811481

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Emphasizing the connection between mathematical objects and their practical C++ implementation, this book provides a comprehensive introduction to both the theory behind the objects and the C and C++ programming. Object-oriented implementation of three-dimensional meshes facilitates understanding of their mathematical nature. Requiring no prerequisites, the text covers discrete mathematics, data structures, and computational physics, including high-order discretization of nonlinear equations. Exercises and solutions make the book suitable for classroom use and a supporting website supplies downloadable code.

Programming for Computations - Python

Author: Svein Linge

Publisher: Springer

Published: 2016-07-25

Total Pages: 244

ISBN-13: 3319324284

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This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.

Implementing Models of Financial Derivatives

Author: Nick Webber

Publisher: John Wiley & Sons

Published: 2011-09-07

Total Pages: 772

ISBN-13: 0470661844

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Implementing Models of Financial Derivatives is a comprehensive treatment of advanced implementation techniques in VBA for models of financial derivatives. Aimed at readers who are already familiar with the basics of VBA it emphasizes a fully object oriented approach to valuation applications, chiefly in the context of Monte Carlo simulation but also more broadly for lattice and PDE methods. Its unique approach to valuation, emphasizing effective implementation from both the numerical and the computational perspectives makes it an invaluable resource. The book comes with a library of almost a hundred Excel spreadsheets containing implementations of all the methods and models it investigates, including a large number of useful utility procedures. Exercises structured around four application streams supplement the exposition in each chapter, taking the reader from basic procedural level programming up to high level object oriented implementations. Written in eight parts, parts 1-4 emphasize application design in VBA, focused around the development of a plain Monte Carlo application. Part 5 assesses the performance of VBA for this application, and the final 3 emphasize the implementation of a fast and accurate Monte Carlo method for option valuation. Key topics include: ?Fully polymorphic factories in VBA; ?Polymorphic input and output using the TextStream and FileSystemObject objects; ?Valuing a book of options; ?Detailed assessment of the performance of VBA data structures; ?Theory, implementation, and comparison of the main Monte Carlo variance reduction methods; ?Assessment of discretization methods and their application to option valuation in models like CIR and Heston; ?Fast valuation of Bermudan options by Monte Carlo. Fundamental theory and implementations of lattice and PDE methods are presented in appendices and developed through the book in the exercise streams. Spanning the two worlds of academic theory and industrial practice, this book is not only suitable as a classroom text in VBA, in simulation methods, and as an introduction to object oriented design, it is also a reference for model implementers and quants working alongside derivatives groups. Its implementations are a valuable resource for students, teachers and developers alike. Note: CD-ROM/DVD and other supplementary materials are not included as part of eBook file.

C++ and Object-Oriented Numeric Computing for Scientists and Engineers

Author: Daoqi Yang

Publisher: Springer Science & Business Media

Published: 2011-06-28

Total Pages: 440

ISBN-13: 1461301890

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This book is an easy, concise but fairly complete introduction to ISO/ANSI C++ with special emphasis on object-oriented numeric computation. A user-defined numeric linear algebra library accompanies the book and can be downloaded from the web.

Numerical Algorithms

Author: Justin Solomon

Publisher: CRC Press

Published: 2015-06-24

Total Pages: 400

ISBN-13: 1482251892

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Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig

An Introduction to C++ and Numerical Methods

Author: James M. Ortega

Publisher: Oxford University Press on Demand

Published: 1999

Total Pages: 273

ISBN-13: 9780195117677

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An introduction to C++ providing explanations of the basics of numerical methods, scientific computing and the basic constructs of C++. Subsequent chapters revisit these topics to treat them in more detail. It also covers numerical methods used in scientific and engineering computation.