Numerical Methods with MATLAB

Implementations and Applications

Author: Gerald W. Recktenwald

Publisher: Pearson College Division

ISBN: N.A

Category: Computers

Page: 786

View: 2324

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This thorough, modern exposition of classic numerical methods using MATLAB briefly develops the fundamental theory of each method. Rather than providing a detailed numerical analysis, the behavior of the methods is exposed by carefully designed numerical experiments. The methods are then exercised on several nontrivial example problems from engineering practice. This structured, concise, and efficient book contains a large number of examples of two basic types—One type of example demonstrates a principle or numerical method in the simplest possible terms. Another type of example demonstrates how a particular method can be used to solve a more complex practical problem. The material in each chapter is organized as a progression from the simple to the complex. Contains an extensive reference to using MATLAB. This includes interactive (command line) use of MATLAB, MATLAB programming, plotting, file input and output. For a practical and rigorous introduction to the fundamentals of numerical computation.
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Numerical Methods for Structured Matrices and Applications

The Georg Heinig Memorial Volume

Author: Dario Andrea Bini,Volker Mehrmann,Vadim Olshevsky,Eugene Tyrtsyhnikov,Marc van Barel

Publisher: Springer Science & Business Media

ISBN: 9783764389963

Category: Mathematics

Page: 439

View: 9125

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This cross-disciplinary volume brings together theoretical mathematicians, engineers and numerical analysts and publishes surveys and research articles related to topics such as fast algorithms, in which the late Georg Heinig made outstanding achievements.
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Numerical Methods and Applications

6th International Conference, NMA 2006, Borovets, Bulgaria, August 20-24, 2006, Revised Papers

Author: Todor Boyanov,Stefka Dimova,Krassimir Georgiev,Geno Nikolov

Publisher: Springer Science & Business Media

ISBN: 3540709401

Category: Computers

Page: 728

View: 6472

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This book constitutes the thoroughly refereed post-proceedings of NMA 2006 held in Borovets, Bulgaria. Coverage in the 84 revised full papers includes numerical methods for hyperbolic problems, robust preconditioning solution methods, metaheuristics for optimization problems, uncertain/control systems and reliable numerics, interpolation and quadrature processes, and large-scale computations in environmental modeling.
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BPR

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 3877

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Numerical Analysis and Its Applications

Second International Conference, NAA 2000 Rousse, Bulgaria, June 11-15, 2000. Revised Papers

Author: Lubin Vulkov,Jerzy Wasniewski,Plamen Yalamov

Publisher: Springer

ISBN: 3540452621

Category: Mathematics

Page: 790

View: 6767

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This book constitutes the thoroughly refereed post-proceedings of the Second International Conference on Numerical Analysis and Its Applications, NAA 2000, held in Rousse, Bulgaria in June 2000.The 90 revised papers presented were carefully selected for inclusion in the book during the two rounds of inspection and reviewing. All current aspects of numerical analysis are addressed. Among the application fields covered are computational sciences and engineering, chemistry, physics, economics, simulation, etc.
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Numerical Analysis with Applications in Mechanics and Engineering

Author: Petre Teodorescu,Nicolae-Doru Stanescu,Nicolae Pandrea

Publisher: John Wiley & Sons

ISBN: 1118614623

Category: Computers

Page: 646

View: 1359

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A much-needed guide on how to use numerical methods to solvepractical engineering problems Bridging the gap between mathematics and engineering,Numerical Analysis with Applications in Mechanics andEngineering arms readers with powerful tools for solvingreal-world problems in mechanics, physics, and civil and mechanicalengineering. Unlike most books on numerical analysis, thisoutstanding work links theory and application, explains themathematics in simple engineering terms, and clearly demonstrateshow to use numerical methods to obtain solutions and interpretresults. Each chapter is devoted to a unique analytical methodology,including a detailed theoretical presentation and emphasis onpractical computation. Ample numerical examples and applicationsround out the discussion, illustrating how to work out specificproblems of mechanics, physics, or engineering. Readers will learnthe core purpose of each technique, develop hands-onproblem-solving skills, and get a complete picture of the studiedphenomenon. Coverage includes: How to deal with errors in numerical analysis Approaches for solving problems in linear and nonlinearsystems Methods of interpolation and approximation of functions Formulas and calculations for numerical differentiation andintegration Integration of ordinary and partial differential equations Optimization methods and solutions for programmingproblems Numerical Analysis with Applications in Mechanics andEngineering is a one-of-a-kind guide for engineers usingmathematical models and methods, as well as for physicists andmathematicians interested in engineering problems.
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Computational Mathematics

Models, Methods, and Analysis with MATLAB and MPI

Author: Robert E. White

Publisher: CRC Press

ISBN: 9780203494479

Category: Mathematics

Page: 408

View: 7955

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Computational Mathematics: Models, Methods, and Analysis with MATLAB and MPI explores and illustrates this process. Each section of the first six chapters is motivated by a specific application. The author applies a model, selects a numerical method, implements computer simulations, and assesses the ensuing results. These chapters include an abundance of MATLAB code. By studying the code instead of using it as a "black box, " you take the first step toward more sophisticated numerical modeling. The last four chapters focus on multiprocessing algorithms implemented using message passing interface (MPI). These chapters include Fortran 9x codes that illustrate the basic MPI subroutines and revisit the applications of the previous chapters from a parallel implementation perspective. All of the codes are available for download from www4.ncsu.edu./~white. This book is not just about math, not just about computing, and not just about applications, but about all three--in other words, computational science. Whether used as an undergraduate textbook, for self-study, or for reference, it builds the foundation you need to make numerical modeling and simulation integral parts of your investigational toolbox.
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Numerical Methods for Chemical Engineering

Applications in MATLAB

Author: Kenneth J Beers,Kenneth J. Beers

Publisher: Cambridge University Press

ISBN: 9780521859714

Category: Juvenile Nonfiction

Page: 474

View: 2690

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Applications of numerical mathematics and scientific computing to chemical engineering.
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Numerical Analysis and Graphic Visualization with MATLAB

Author: Shoichiro Nakamura

Publisher: Prentice Hall

ISBN: 9780130654892

Category: Computers

Page: 519

View: 415

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PREFACE WHAT THIS BOOK DESCRIBES This book is intended to introduce numerical analysis and graphic visualization using MATLAB to college students majoring in engineering and science.It can also be a handbook of MATLAB applications for professional engi-neers and scientists. The goal is not to teach the mathematics of numericalanalysis, but rather to teach the knowledge and skills of solving equationsand presenting them graphically so that readers can easily handle equationsand results of the computations. With its unique and fascinating capabilities, MATLAB has changed theconcept of programming for numerical and mathematical analyses. Therefore, MATLAB is a superb vehicle to achieve our goal. This book fullyimplements the mathematical and graphic tools in the most recent versionof MATLAB. The following four fundamental elements are integrated in this book: (1)programming in MATLAB, (2) mathematical basics of numerical analysis,(3) application of numerical methods to engineering, scientific, and mathematical problems, and (4) scientific graphics with MATLAB. The first two chapters are comprehensive tutorials of MATLAB commands and graphic tools, particularly for the beginner or entry-level collegestudent. Indeed, these two chapters have been most significantly enhancedin this edition compared to the first edition. In Chapter 1, understandingand developing programming skills on MATLAB are emphasized particularlybecause, unless the reader has knowledge and experience with another pro-gramming language, these are tough hurdles for the beginner to overcome.To acquire the knowledge and skills necessary to read the rest of the book,solving the problems at the end of each chapter is very important. Chapter 2 starts out with the elements of graphics on MATLAB, whichis easy to follow. Yet, toward the end of the chapter, three-dimensionalgraphics on the professional level are achieved. Not only is the programmingtechnique of plotting functions mentioned, but also skills of presenting mathematical and scientific material using graphics are developed throughout thechapter. The graphics knowledge acquired in this chapter are foundationsin learning and applying the numerical methods described in the remainderof the book. Again, practice on the computer is important. Some studentstry to memorize scripts without understanding why and how they work,but such an effort is utterly meaningless. More important is to play with afew new commands, understand how they work and how they may fail, andfinally become a master of the commands. Chapters 3 through 11 cover numerical methods and their implementations with MATLAB. All the numerical methods described are illustratedwith applications on MATLAB. Appendices describe special topics, including advanced three-dimensional graphics with colors, motion pictures, imageprocessing, and graphical user interface. Readers should feel free to use thescripts in this book in any way desired. However, the beginning studentsare advised not to u se these scripts blindly. The students should write theirown scripts. Using the lists of the scripts and function, readers can run most examples and figures on their own computers. The m-files of the scripts can bedownloaded as mentioned later. WHAT IS UNIQUE ABOUT MATLAB? MATLAB may be regarded as a programming language like Fortran or C,although describing it in a few words is difficult. Some of its outstandingfeatures for numerical analyses, however, are: Significantly simpler programming Continuity among integer, real, and complex values Extended range of numbers and their accuracy A comprehensive mathematical library Extensive graphic tools including graphic user interface functions Capability of linking with traditional programming languages Transportability of MATLAB programs An extraordinary feature of MATLAB is that there is no distinction amongreal, complex, and integer numbers. All numbers are in double precision. InMATLAB, all kinds of numbers are continuously connected, as they should be. It means that in MATLAB, any variable can take any type of numberwithout special declaration in programming. This makes programming fasterand more productive. In Fortran, a different subroutine is necessary for eachsingle, double, real or complex, or integer variable, while in MATLAB thereis no need to separate them. The mathematical library in MATLAB makes mathematical analyseseasy. Yet the user can develop additional mathematical routines significantlymore easily than in other programming languages because of the continuitybetween real and complex variables. Among numerous mathematical functions, linear algebra solvers play central roles. Indeed, the whole MATLABsystem is founded upon linear algebra solvers. IMPORTANCE OF GRAPHICS Graphic presentation of mathematical analysis helps the reader to under-stand mathematics and makes it enjoyable. Although this advantage hasbeen well known, presenting computed results with computer graphics wasnot without substantial extra effort in the past. With MATLAB, however,graphic presentations of mathematical material is possible with just a fewcommands. Scientific and even artistic graphic objects can be created on thescreen using mathematical expressions. It has been found that MATLABgraphics motivate and excite students to learn mathematical and numericalmethods that could otherwise be dull. MATLAB graphics are easy and great fun for readers. This book alsoillustrates image processing and production of motion pictures for scientific computing as well as for artistic or hobby material. WILL MATLAB ELIMINATE THE NEED FOR FORTRAN OR C? The answer is no. Fortran and C are still important for high-performancecomputing that requires a large memory or long computing time. The speedof MATLAB computation is significantly slower than that with Fortran orC because MATLAB is paying the high price for the nice features. Learn-ing Fortran or C, however, is not a prerequisite for understanding MATLAB. REFERENCE BOOKS THAT ARE HELPFUL TO LEARN MATLAB This book explains many MATLAB commands but is not intended to be acomplete guide to MATLAB. Readers interested in further information onMATLAB are advised to read User's Guide and Reference Guide. Also, youshould know that over 400 books for use with MATLAB, Simulink, Tool-boxes, and Blocksets have been written. See http://www.mathworks.com/support/books WEB SITE FOR READERS OF THIS BOOK A Web site for readers of this book has been opened at http://olen.eng.ohio-state.ed/matlab This Web site includes additional examples, hints, and color graphics thatcannot be printed in the book. If there are corrections to the text material,they will appear on this Web site. Links to other relevant sites are alsoprovided. HOW TO OBTAIN M-FILES PACKAGE The m-files package that includes all the scripts and functions developed inthe present book are available from the download site of the publisher, whichcan be accessed via the Web site in the foregoing paragraph. The packageincludes the following files: All m-files listed at the end of chapters. All scripts illustrated in the book (except short ones). Scripts to plot typical figures in the book. SOLUTION KEYS Solution keys for the problems for each chapter are available at the end ofthis book. Further help may also be available at the Web site for the readers. HOW TO OBTAIN MORE INFORMATION ABOUT MATLAB The best way to start collecting more information about MATLAB is to visitthe Web site of MATHWORKS athttp://www.mathworks.com For other communication with MathWorks, their address is: The MathWorks, Inc., 3 Apple Hill Drive, Natick ,MA 01760-2098, United StatesPhone: 508-647-7000, Fax: 508-647-7001. LIST OF REVIEWERS The first edition of this book was reviewed by: Professor T. Aldemir, Nuclear Engineering, The Ohio State University, Columbus, Ohio Professor M. Darwish, Mechanical Engineering Department, American University of Beirut, Beirut, Lebanon The MathWorks Inc., Natick, Massacusetts Professor J.K. Shultis, Nuclear Engineering, Kansas State University, Manhattan, Kansas Professor S.V. Sreenivasan, Department of Mechanical Engineering, University of Texas, Austin, Texas
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Financial Modelling

Theory, Implementation and Practice with MATLAB Source

Author: Joerg Kienitz,Daniel Wetterau

Publisher: John Wiley & Sons

ISBN: 0470744898

Category: Business & Economics

Page: 734

View: 2576

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Financial modelling Theory, Implementation and Practice with Matlab Source Jörg Kienitz and Daniel Wetterau Financial Modelling - Theory, Implementation and Practice with MATLAB Source is a unique combination of quantitative techniques, the application to financial problems and programming using Matlab. The book enables the reader to model, design and implement a wide range of financial models for derivatives pricing and asset allocation, providing practitioners with complete financial modelling workflow, from model choice, deriving prices and Greeks using (semi-) analytic and simulation techniques, and calibration even for exotic options. The book is split into three parts. The first part considers financial markets in general and looks at the complex models needed to handle observed structures, reviewing models based on diffusions including stochastic-local volatility models and (pure) jump processes. It shows the possible risk-neutral densities, implied volatility surfaces, option pricing and typical paths for a variety of models including SABR, Heston, Bates, Bates-Hull-White, Displaced-Heston, or stochastic volatility versions of Variance Gamma, respectively Normal Inverse Gaussian models and finally, multi-dimensional models. The stochastic-local-volatility Libor market model with time-dependent parameters is considered and as an application how to price and risk-manage CMS spread products is demonstrated. The second part of the book deals with numerical methods which enables the reader to use the models of the first part for pricing and risk management, covering methods based on direct integration and Fourier transforms, and detailing the implementation of the COS, CONV, Carr-Madan method or Fourier-Space-Time Stepping. This is applied to pricing of European, Bermudan and exotic options as well as the calculation of the Greeks. The Monte Carlo simulation technique is outlined and bridge sampling is discussed in a Gaussian setting and for Lévy processes. Computation of Greeks is covered using likelihood ratio methods and adjoint techniques. A chapter on state-of-the-art optimization algorithms rounds up the toolkit for applying advanced mathematical models to financial problems and the last chapter in this section of the book also serves as an introduction to model risk. The third part is devoted to the usage of Matlab, introducing the software package by describing the basic functions applied for financial engineering. The programming is approached from an object-oriented perspective with examples to propose a framework for calibration, hedging and the adjoint method for calculating Greeks in a Libor market model. Source code used for producing the results and analysing the models is provided on the author's dedicated website, http://www.mathworks.de/matlabcentral/fileexchange/authors/246981.
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