Numerical Algorithms

Author : Justin Solomon
Publisher : CRC Press
ISBN 13 : 1482251892
Total Pages : 400 pages
Book Rating : 4.90/5 ( download)

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Download or read book Numerical Algorithms written by Justin Solomon and published by CRC Press. This book was released on 2015-06-24 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Nicholas J. Higham
Publisher : SIAM
ISBN 13 : 9780898718027
Total Pages : 710 pages
Book Rating : 4.23/5 ( download)

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Download or read book Accuracy and Stability of Numerical Algorithms written by Nicholas J. Higham and published by SIAM. This book was released on 2002-01-01 with total page 710 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accuracy and Stability of Numerical Algorithms gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. This second edition expands and updates the coverage of the first edition (1996) and includes numerous improvements to the original material. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing LU factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures.

Author : Giesela Engeln-Müllges
Publisher : Springer Science & Business Media
ISBN 13 : 3642610749
Total Pages : 610 pages
Book Rating : 4.45/5 ( download)

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Download or read book Numerical Algorithms with C written by Giesela Engeln-Müllges and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: More scientists now use C than any other programming language. This book contains practical, computer-ready algorithms for many standard methods of numerical mathematics. It describes the principles of the various methods and provides support in choosing the appropriate method for a given task. Topics given special emphasis include converging methods for solving nonlinear equations, methods for solving systems of linear equations for many special matrix structures, and the Shepard method for multidimensional interpolation. The CD contains C-programs for almost all the algorithms given in the book and a compiler, together with software for graphical printing.

Author : Anne Greenbaum
Publisher : Princeton University Press
ISBN 13 : 1400842670
Total Pages : 471 pages
Book Rating : 4.74/5 ( download)

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Download or read book Numerical Methods written by Anne Greenbaum and published by Princeton University Press. This book was released on 2012-04-01 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous and comprehensive introduction to numerical analysis Numerical Methods provides a clear and concise exploration of standard numerical analysis topics, as well as nontraditional ones, including mathematical modeling, Monte Carlo methods, Markov chains, and fractals. Filled with appealing examples that will motivate students, the textbook considers modern application areas, such as information retrieval and animation, and classical topics from physics and engineering. Exercises use MATLAB and promote understanding of computational results. The book gives instructors the flexibility to emphasize different aspects—design, analysis, or computer implementation—of numerical algorithms, depending on the background and interests of students. Designed for upper-division undergraduates in mathematics or computer science classes, the textbook assumes that students have prior knowledge of linear algebra and calculus, although these topics are reviewed in the text. Short discussions of the history of numerical methods are interspersed throughout the chapters. The book also includes polynomial interpolation at Chebyshev points, use of the MATLAB package Chebfun, and a section on the fast Fourier transform. Supplementary materials are available online. Clear and concise exposition of standard numerical analysis topics Explores nontraditional topics, such as mathematical modeling and Monte Carlo methods Covers modern applications, including information retrieval and animation, and classical applications from physics and engineering Promotes understanding of computational results through MATLAB exercises Provides flexibility so instructors can emphasize mathematical or applied/computational aspects of numerical methods or a combination Includes recent results on polynomial interpolation at Chebyshev points and use of the MATLAB package Chebfun Short discussions of the history of numerical methods interspersed throughout Supplementary materials available online

Author : Peter Bürgisser
Publisher : Springer Science & Business Media
ISBN 13 : 3642388965
Total Pages : 567 pages
Book Rating : 4.65/5 ( download)

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Download or read book Condition written by Peter Bürgisser and published by Springer Science & Business Media. This book was released on 2013-08-15 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers threads that have evolved across different mathematical disciplines into seamless narrative. It deals with condition as a main aspect in the understanding of the performance ---regarding both stability and complexity--- of numerical algorithms. While the role of condition was shaped in the last half-century, so far there has not been a monograph treating this subject in a uniform and systematic way. The book puts special emphasis on the probabilistic analysis of numerical algorithms via the analysis of the corresponding condition. The exposition's level increases along the book, starting in the context of linear algebra at an undergraduate level and reaching in its third part the recent developments and partial solutions for Smale's 17th problem which can be explained within a graduate course. Its middle part contains a condition-based course on linear programming that fills a gap between the current elementary expositions of the subject based on the simplex method and those focusing on convex programming.

Author : Thomas S. Parker
Publisher : Springer Science & Business Media
ISBN 13 : 1461234867
Total Pages : 354 pages
Book Rating : 4.69/5 ( download)

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Download or read book Practical Numerical Algorithms for Chaotic Systems written by Thomas S. Parker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the basic tenets of science is that deterministic systems are completely predictable-given the initial condition and the equations describing a system, the behavior of the system can be predicted 1 for all time. The discovery of chaotic systems has eliminated this viewpoint. Simply put, a chaotic system is a deterministic system that exhibits random behavior. Though identified as a robust phenomenon only twenty years ago, chaos has almost certainly been encountered by scientists and engi neers many times during the last century only to be dismissed as physical noise. Chaos is such a wide-spread phenomenon that it has now been reported in virtually every scientific discipline: astronomy, biology, biophysics, chemistry, engineering, geology, mathematics, medicine, meteorology, plasmas, physics, and even the social sci ences. It is no coincidence that during the same two decades in which chaos has grown into an independent field of research, computers have permeated society. It is, in fact, the wide availability of inex pensive computing power that has spurred much of the research in chaotic dynamics. The reason is simple: the computer can calculate a solution of a nonlinear system. This is no small feat. Unlike lin ear systems, where closed-form solutions can be written in terms of the system's eigenvalues and eigenvectors, few nonlinear systems and virtually no chaotic systems possess closed-form solutions.

Author : Forman S. Acton
Publisher : American Mathematical Soc.
ISBN 13 : 147045727X
Total Pages : 549 pages
Book Rating : 4.73/5 ( download)

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Download or read book Numerical Methods that Work written by Forman S. Acton and published by American Mathematical Soc.. This book was released on 2020-07-31 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Karim Belabas
Publisher : American Mathematical Soc.
ISBN 13 : 1470463512
Total Pages : 429 pages
Book Rating : 4.19/5 ( download)

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Download or read book Numerical Algorithms for Number Theory: Using Pari/GP written by Karim Belabas and published by American Mathematical Soc.. This book was released on 2021-06-23 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents multiprecision algorithms used in number theory and elsewhere, such as extrapolation, numerical integration, numerical summation (including multiple zeta values and the Riemann-Siegel formula), evaluation and speed of convergence of continued fractions, Euler products and Euler sums, inverse Mellin transforms, and complex L L-functions. For each task, many algorithms are presented, such as Gaussian and doubly-exponential integration, Euler-MacLaurin, Abel-Plana, Lagrange, and Monien summation. Each algorithm is given in detail, together with a complete implementation in the free Pari/GP system. These implementations serve both to make even more precise the inner workings of the algorithms, and to gently introduce advanced features of the Pari/GP language. This book will be appreciated by anyone interested in number theory, specifically in practical implementations, computer experiments and numerical algorithms that can be scaled to produce thousands of digits of accuracy.

Author : Gisela Engeln-Müllges
Publisher : Springer
ISBN 13 : 9783642800450
Total Pages : 602 pages
Book Rating : 4.59/5 ( download)

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Download or read book Numerical Algorithms with Fortran written by Gisela Engeln-Müllges and published by Springer. This book was released on 2014-04-13 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a completely up-to-date compendium of Fortran algorithms for numerical mathematics, including many sophisticated algorithms which are not available elsewhere. All have been extensively field-tested and cover methods for solving nonlinear equations, the method of Laguerre for solving algebraic equations, conjugating gradients for solving linear systems of equations, and the McKee algorithm for solving special systems of symmetric equations. The real, practical algorithms provided make the book indispensable for applied scientists working in all areas of research. The CD contains Fortran programs for the algorithms given in the text.

Author : Santanu Saha Ray
Publisher : CRC Press
ISBN 13 : 1498741835
Total Pages : 391 pages
Book Rating : 4.35/5 ( download)

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Download or read book Numerical Analysis with Algorithms and Programming written by Santanu Saha Ray and published by CRC Press. This book was released on 2018-09-03 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Analysis with Algorithms and Programming is the first comprehensive textbook to provide detailed coverage of numerical methods, their algorithms, and corresponding computer programs. It presents many techniques for the efficient numerical solution of problems in science and engineering. Along with numerous worked-out examples, end-of-chapter exercises, and Mathematica® programs, the book includes the standard algorithms for numerical computation: Root finding for nonlinear equations Interpolation and approximation of functions by simpler computational building blocks, such as polynomials and splines The solution of systems of linear equations and triangularization Approximation of functions and least square approximation Numerical differentiation and divided differences Numerical quadrature and integration Numerical solutions of ordinary differential equations (ODEs) and boundary value problems Numerical solution of partial differential equations (PDEs) The text develops students’ understanding of the construction of numerical algorithms and the applicability of the methods. By thoroughly studying the algorithms, students will discover how various methods provide accuracy, efficiency, scalability, and stability for large-scale systems.