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Numerical Computations: Theory and Algorithms

Author : Yaroslav D. Sergeyev

Publisher : Springer Nature

Page : 550 pages

File Size : 36,39 MB

Release : 2020-02-13

Category : Computers

ISBN : 3030406164

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Book Description

The two-volume set LNCS 11973 and 11974 constitute revised selected papers from the Third International Conference on Numerical Computations: Theory and Algorithms, NUMTA 2019, held in Crotone, Italy, in June 2019. This volume, LNCS 11974, consists of 19 full and 32 short papers chosen among regular papers presented at the the Conference including also the paper of the winner (Lorenzo Fiaschi, Pisa, Italy) of The Springer Young Researcher Prize for the best NUMTA 2019 presentation made by a young scientist. The papers in part II explore the advanced research developments in such interconnected fields as local and global optimization, machine learning, approximation, and differential equations. A special focus is given to advanced ideas related to methods and applications using emerging computational paradigms.



Numerical Analysis with Algorithms and Programming

Author : Santanu Saha Ray

Publisher : CRC Press

Page : 708 pages

File Size : 43,69 MB

Release : 2018-09-03

Category : Mathematics

ISBN : 131536221X

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Book Description

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.



Numerical Algorithms

Author : Justin Solomon

Publisher : CRC Press

Page : 400 pages

File Size : 30,59 MB

Release : 2015-06-24

Category : Computers

ISBN : 1482251892

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Book Description

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



Numerical Algorithms for Number Theory: Using Pari/GP

Author : Karim Belabas

Publisher : American Mathematical Soc.

Page : 429 pages

File Size : 28,54 MB

Release : 2021-06-23

Category : Education

ISBN : 1470463512

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Book Description

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.



Numerical Computations: Theory and Algorithms

Author : Yaroslav D. Sergeyev

Publisher : Springer Nature

Page : 634 pages

File Size : 38,52 MB

Release : 2020-02-13

Category : Computers

ISBN : 3030390810

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Book Description

The two-volume set LNCS 11973 and 11974 constitute revised selected papers from the Third International Conference on Numerical Computations: Theory and Algorithms, NUMTA 2019, held in Crotone, Italy, in June 2019. This volume, LNCS 11973, consists of 34 full and 18 short papers chosen among papers presented at special streams and sessions of the Conference. The papers in part I were organized following the topics of these special sessions: approximation: methods, algorithms, and applications; computational methods for data analysis; first order methods in optimization: theory and applications; high performance computing in modelling and simulation; numbers, algorithms, and applications; optimization and management of water supply.



Numerical Analysis

Author : Larkin Ridgway Scott

Publisher : Princeton University Press

Page : 342 pages

File Size : 47,32 MB

Release : 2011-04-18

Category : Mathematics

ISBN : 1400838967

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Book Description

Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and self-contained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software, including complete details that are missing from most textbooks. Using an inquiry-based learning approach, Numerical Analysis is written in a narrative style, provides historical background, and includes many of the proofs and technical details in exercises. Students will be able to go beyond an elementary understanding of numerical simulation and develop deep insights into the foundations of the subject. They will no longer have to accept the mathematical gaps that exist in current textbooks. For example, both necessary and sufficient conditions for convergence of basic iterative methods are covered, and proofs are given in full generality, not just based on special cases. The book is accessible to undergraduate mathematics majors as well as computational scientists wanting to learn the foundations of the subject. Presents the mathematical foundations of numerical analysis Explains the mathematical details behind simulation software Introduces many advanced concepts in modern analysis Self-contained and mathematically rigorous Contains problems and solutions in each chapter Excellent follow-up course to Principles of Mathematical Analysis by Rudin



Accuracy and Stability of Numerical Algorithms

Author : Nicholas J. Higham

Publisher : SIAM

Page : 710 pages

File Size : 26,98 MB

Release : 2002-01-01

Category : Mathematics

ISBN : 9780898718027

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Book Description

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.



Numerical Methods in Scientific Computing

Author : Germund Dahlquist

Publisher : SIAM

Page : 742 pages

File Size : 21,47 MB

Release : 2008-01-01

Category : Mathematics

ISBN : 0898717787

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Book Description

This new book from the authors of the classic book Numerical methods addresses the increasingly important role of numerical methods in science and engineering. More cohesive and comprehensive than any other modern textbook in the field, it combines traditional and well-developed topics with other material that is rarely found in numerical analysis texts, such as interval arithmetic, elementary functions, operator series, convergence acceleration, and continued fractions. Although this volume is self-contained, more comprehensive treatments of matrix computations will be given in a forthcoming volume. A supplementary Website contains three appendices: an introduction to matrix computations; a description of Mulprec, a MATLAB multiple precision package; and a guide to literature, algorithms, and software in numerical analysis. Review questions, problems, and computer exercises are also included. For use in an introductory graduate course in numerical analysis and for researchers who use numerical methods in science and engineering.



Numerical Geometry of Images

Author : Ron Kimmel

Publisher : Springer Science & Business Media

Page : 222 pages

File Size : 37,74 MB

Release : 2012-09-07

Category : Computers

ISBN : 0387216375

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Book Description

Numerical Geometry of Images examines computational methods and algorithms in image processing. It explores applications like shape from shading, color-image enhancement and segmentation, edge integration, offset curve computation, symmetry axis computation, path planning, minimal geodesic computation, and invariant signature calculation. In addition, it describes and utilizes tools from mathematical morphology, differential geometry, numerical analysis, and calculus of variations. Graduate students, professionals, and researchers with interests in computational geometry, image processing, computer graphics, and algorithms will find this new text / reference an indispensable source of insight of instruction.



A First Course in Numerical Methods

Author : Uri M. Ascher

Publisher : SIAM

Page : 574 pages

File Size : 37,18 MB

Release : 2011-07-14

Category : Mathematics

ISBN : 0898719976

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Book Description

Offers students a practical knowledge of modern techniques in scientific computing.