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Numerical Analysis

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Numerical Analysis

Numerical Analysis Book
Author : Rainer Kress
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1461205999
Language : En, Es, Fr & De

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Book Description :

An introduction into numerical analysis for students in mathematics, physics, and engineering. Instead of attempting to exhaustively cover everything, the goal is to guide readers towards the basic ideas and general principles by way of the main and important numerical methods. The book includes the necessary basic functional analytic tools for the solid mathematical foundation of numerical analysis -- indispensable for any deeper study and understanding of numerical methods, in particular, for differential equations and integral equations. The text is presented in a concise and easily understandable fashion so as to be successfully mastered in a one-year course.

Numerical Analysis for Statisticians

Numerical Analysis for Statisticians Book
Author : Kenneth Lange
Publisher : Springer Science & Business Media
Release : 2010-06-15
ISBN : 1441959440
Language : En, Es, Fr & De

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Book Description :

Numerical analysis is the study of computation and its accuracy, stability and often its implementation on a computer. This book focuses on the principles of numerical analysis and is intended to equip those readers who use statistics to craft their own software and to understand the advantages and disadvantages of different numerical methods.

Analysis of Numerical Methods

Analysis of Numerical Methods Book
Author : Eugene Isaacson,Herbert Bishop Keller
Publisher : Courier Corporation
Release : 2012-04-26
ISBN : 0486137988
Language : En, Es, Fr & De

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Book Description :

This excellent text for advanced undergraduate and graduate students covers norms, numerical solutions of linear systems and matrix factoring, eigenvalues and eigenvectors, polynomial approximation, and more. Many examples and problems. 1966 edition.

Numerical Analysis

Numerical Analysis Book
Author : David Ronald Kincaid,Elliott Ward Cheney
Publisher : American Mathematical Soc.
Release : 2002
ISBN : 0821847880
Language : En, Es, Fr & De

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Book Description :

This book introduces students with diverse backgrounds to various types of mathematical analysis that are commonly needed in scientific computing. The subject of numerical analysis is treated from a mathematical point of view, offering a complete analysis of methods for scientific computing with appropriate motivations and careful proofs. In an engaging and informal style, the authors demonstrate that many computational procedures and intriguing questions of computer science arise from theorems and proofs. Algorithms are presented in pseudocode, so that students can immediately write computer programs in standard languages or use interactive mathematical software packages. This book occasionally touches upon more advanced topics that are not usually contained in standard textbooks at this level.

Introduction to Numerical Analysis and Scientific Computing

Introduction to Numerical Analysis and Scientific Computing Book
Author : Nabil Nassif,Dolly Khuwayri Fayyad
Publisher : CRC Press
Release : 2013-08-05
ISBN : 1466589485
Language : En, Es, Fr & De

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Book Description :

Designed for a one-semester course, Introduction to Numerical Analysis and Scientific Computing presents fundamental concepts of numerical mathematics and explains how to implement and program numerical methods. The classroom-tested text helps students understand floating point number representations, particularly those pertaining to IEEE simple and double-precision standards as used in scientific computer environments such as MATLAB® version 7. Drawing on their years of teaching students in mathematics, engineering, and the sciences, the authors discuss computer arithmetic as a source for generating round-off errors and how to avoid the use of algebraic expression that may lead to loss of significant figures. They cover nonlinear equations, linear algebra concepts, the Lagrange interpolation theorem, numerical differentiation and integration, and ODEs. They also focus on the implementation of the algorithms using MATLAB®. Each chapter ends with a large number of exercises, with answers to odd-numbered exercises provided at the end of the book. Throughout the seven chapters, several computer projects are proposed. These test the students' understanding of both the mathematics of numerical methods and the art of computer programming.

INTRODUCTORY METHODS OF NUMERICAL ANALYSIS

INTRODUCTORY METHODS OF NUMERICAL ANALYSIS Book
Author : S. S. SASTRY
Publisher : PHI Learning Pvt. Ltd.
Release : 2012-06-12
ISBN : 8120345924
Language : En, Es, Fr & De

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Book Description :

This thoroughly revised and updated text, now in its fifth edition, continues to provide a rigorous introduction to the fundamentals of numerical methods required in scientific and technological applications, emphasizing on teaching students numerical methods and in helping them to develop problem-solving skills. While the essential features of the previous editions such as References to MATLAB, IMSL, Numerical Recipes program libraries for implementing the numerical methods are retained, a chapter on Spline Functions has been added in this edition because of their increasing importance in applications. This text is designed for undergraduate students of all branches of engineering. NEW TO THIS EDITION : Includes additional modified illustrative examples and problems in every chapter. Provides answers to all chapter-end exercises. Illustrates algorithms, computational steps or flow charts for many numerical methods. Contains four model question papers at the end of the text.

Numerical Analysis or Numerical Method in Symmetry

Numerical Analysis or Numerical Method in Symmetry Book
Author : Clemente Cesarano
Publisher : MDPI
Release : 2020-02-21
ISBN : 3039283723
Language : En, Es, Fr & De

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Book Description :

This Special Issue focuses mainly on techniques and the relative formalism typical of numerical methods and therefore of numerical analysis, more generally. These fields of study of mathematics represent an important field of investigation both in the field of applied mathematics and even more exquisitely in the pure research of the theory of approximation and the study of polynomial relations as well as in the analysis of the solutions of the differential equations both ordinary and partial derivatives. Therefore, a substantial part of research on the topic of numerical analysis cannot exclude the fundamental role played by approximation theory and some of the tools used to develop this research. In this Special Issue, we want to draw attention to the mathematical methods used in numerical analysis, such as special functions, orthogonal polynomials, and their theoretical tools, such as Lie algebra, to study the concepts and properties of some special and advanced methods, which are useful in the description of solutions of linear and nonlinear differential equations. A further field of investigation is dedicated to the theory and related properties of fractional calculus with its adequate application to numerical methods.

Elements of Numerical Analysis

Elements of Numerical Analysis Book
Author : Radhey S. Gupta
Publisher : Cambridge University Press
Release : 2015-05-14
ISBN : 1107500494
Language : En, Es, Fr & De

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Book Description :

This textbook provides detailed discussion on fundamental concepts and applications of numerical analysis.

Advances in Optimization and Numerical Analysis

Advances in Optimization and Numerical Analysis Book
Author : S. Gomez,J.P. Hennart
Publisher : Springer
Release : 2010-12-05
ISBN : 9789048143580
Language : En, Es, Fr & De

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Book Description :

In January 1992, the Sixth Workshop on Optimization and Numerical Analysis was held in the heart of the Mixteco-Zapoteca region, in the city of Oaxaca, Mexico, a beautiful and culturally rich site in ancient, colonial and modern Mexican civiliza tion. The Workshop was organized by the Numerical Analysis Department at the Institute of Research in Applied Mathematics of the National University of Mexico in collaboration with the Mathematical Sciences Department at Rice University, as were the previous ones in 1978, 1979, 1981, 1984 and 1989. As were the third, fourth, and fifth workshops, this one was supported by a grant from the Mexican National Council for Science and Technology, and the US National Science Foundation, as part of the joint Scientific and Technical Cooperation Program existing between these two countries. The participation of many of the leading figures in the field resulted in a good representation of the state of the art in Continuous Optimization, and in an over view of several topics including Numerical Methods for Diffusion-Advection PDE problems as well as some Numerical Linear Algebraic Methods to solve related pro blems. This book collects some of the papers given at this Workshop.

Numerical Analysis

Numerical Analysis Book
Author : Anonim
Publisher : Academic Publishers
Release : 2021-09-26
ISBN : 9788187504481
Language : En, Es, Fr & De

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Book Description :

Download Numerical Analysis book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

New Sinc Methods of Numerical Analysis

New Sinc Methods of Numerical Analysis Book
Author : Gerd Baumann
Publisher : Springer Nature
Release : 2021-09-26
ISBN : 303049716X
Language : En, Es, Fr & De

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Book Description :

Download New Sinc Methods of Numerical Analysis book written by Gerd Baumann, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Classical and Modern Numerical Analysis

Classical and Modern Numerical Analysis Book
Author : Azmy S. Ackleh,Edward James Allen,R. Baker Kearfott,Padmanabhan Seshaiyer
Publisher : Chapman and Hall/CRC
Release : 2009-07-20
ISBN : 9781420091571
Language : En, Es, Fr & De

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Book Description :

Classical and Modern Numerical Analysis: Theory, Methods and Practice provides a sound foundation in numerical analysis for more specialized topics, such as finite element theory, advanced numerical linear algebra, and optimization. It prepares graduate students for taking doctoral examinations in numerical analysis. The text covers the main areas of introductory numerical analysis, including the solution of nonlinear equations, numerical linear algebra, ordinary differential equations, approximation theory, numerical integration, and boundary value problems. Focusing on interval computing in numerical analysis, it explains interval arithmetic, interval computation, and interval algorithms. The authors illustrate the concepts with many examples as well as analytical and computational exercises at the end of each chapter. This advanced, graduate-level introduction to the theory and methods of numerical analysis supplies the necessary background in numerical methods so that students can apply the techniques and understand the mathematical literature in this area. Although the book is independent of a specific computer program, MATLAB® code is available on the authors' website to illustrate various concepts.

Introduction to Numerical Analysis

Introduction to Numerical Analysis Book
Author : J. Stoer,R. Bulirsch
Publisher : Springer Science & Business Media
Release : 2013-04-17
ISBN : 1475755929
Language : En, Es, Fr & De

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Book Description :

This book is based on a one-year introductory course on numerical analysis given by the authors at several universities in Germany and the United States. The authors concentrate on methods which can be worked out on a digital computer. For important topics, algorithmic descriptions (given more or less formally in ALGOL 60), as well as thorough but concise treatments of their theoretical founda tions, are provided. Where several methods for solving a problem are presented, comparisons of their applicability and limitations are offered. Each comparison is based on operation counts, theoretical properties such as convergence rates, and, more importantly, the intrinsic numerical properties that account for the reliability or unreliability of an algorithm. Within this context, the introductory chapter on error analysis plays a special role because it precisely describes basic concepts, such as the numerical stability of algorithms, that are indispensable in the thorough treatment of numerical questions. The remaining seven chapters are devoted to describing numerical methods in various contexts. In addition to covering standard topics, these chapters encom pass some special subjects not usually found in introductions to numerical analysis. Chapter 2, which discusses interpolation, gives an account of modem fast Fourier transform methods. In Chapter 3, extrapolation techniques for spe~d ing up the convergence of discretization methods in connection with Romberg integration are explained at length.

Topics in Numerical Analysis

Topics in Numerical Analysis Book
Author : G. Alefeld,Xiaojun Chen
Publisher : Springer Science & Business Media
Release : 2001-09-11
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

This collection of papers on numerical analysis with special emphasis on nonlinear problems covers a broad spectrum of fields. Several papers are involved in applying numerical methods for proving the existence of solutions of nonlinear problems, e.g. of boundary problems or of obstacle problems. Naturally the solution of linear and nonlinear problems by iterative methods is the subject of a couple of papers. Here topics like the fast verification of solutions of monotone matrix equations, the convergence of linear asynchronous iteration with spectral radius of modulus one or aggregation and disaggregation methods for p-cyclic Markov chains are treated. On the other hand papers involved in optimization problems can be found. Nearly all fields of modern numerical analysis are touched by at least one paper.

A Brief Introduction to Numerical Analysis

A Brief Introduction to Numerical Analysis Book
Author : Evgeniĭ Evgenʹevich Tyrtyshnikov
Publisher : Springer Science & Business Media
Release : 1997
ISBN : 9780817639167
Language : En, Es, Fr & De

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Book Description :

This is an advanced textbook based on lectures delivered at the Moscow Physico-Technical Institute. Brevity, logical organization of the material, and a sometimes lighthearted approach are distinctive features of this modest book. The author makes the reader an active participant by asking questions, hinting, giving direct recommendations, comparing different methods, and discussing "pessimistic" and "optimistic" approaches to numerical analysis in a short time. Since matrix analysis underlies numerical methods and the author is an expert in this field, emphasis in the book is on methods and algorithms of matrix analysis. Also considered are function approximations, methods of solving nonlinear equations and minimization methods. Alongside classical methods, new results and approaches developed over the last few years are discussed - namely those on spectral distribution theory and what it gives for design and proof of modern preconditioning strategies for large-scale linear algebra problems. Advanced students and graduate students majoring in computer science, physics and mathematics will find this book helpful. It can be equally useful for advanced readers and researchers in providing them with new findings and new accessible views of the basic mathematical framework.

Numerical Analysis

Numerical Analysis Book
Author : L. Ridgway Scott
Publisher : Princeton University Press
Release : 2011-04-18
ISBN : 9781400838967
Language : En, Es, Fr & De

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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

Dynamical Systems and Numerical Analysis

Dynamical Systems and Numerical Analysis Book
Author : Andrew Stuart,A. R. Humphries
Publisher : Cambridge University Press
Release : 1998-11-28
ISBN : 9780521645638
Language : En, Es, Fr & De

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Book Description :

The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulated as dynamical systems and the convergence and stability properties of the methods are examined.

Numerical Analysis and Its Applications

Numerical Analysis and Its Applications Book
Author : Ivan Dimov,István Faragó,Lubin Vulkov
Publisher : Springer
Release : 2013-09-27
ISBN : 9783642415142
Language : En, Es, Fr & De

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Book Description :

This book constitutes thoroughly revised selected papers of the 5th International Conference on Numerical Analysis and Its Applications, NAA 2012, held in Lozenetz, Bulgaria, in June 2012. The 65 revised papers presented were carefully reviewed and selected from various submissions. The papers cover a broad area of topics of interest such as numerical approximation and computational geometry; numerical linear algebra and numerical solution of transcendental equation; numerical methods for differential equations; numerical stochastics, numerical modeling; and high performance scientific computing.

Principles and Procedures of Numerical Analysis

Principles and Procedures of Numerical Analysis Book
Author : Ferenc Szidarovszky,Szidarovszky Ferenc,Sidney J. Yakowitz
Publisher : Springer
Release : 1978
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Approximation and interpolation of functions; Numerical differentiation and integration; General theory for iteration methods; Solution of nonlinear equations; The solution of simultaneous linear equations; The solution of matrix eigenvalue problems; The numerical solution of ordinary differential equations; The numerical solution of partial differential equations.

NUMERICAL ANALYSIS WITH ALGORITHMS AND COMPUTER PROGRAMS IN C

NUMERICAL ANALYSIS WITH ALGORITHMS AND COMPUTER PROGRAMS IN C   Book
Author : AJAY WADHWA
Publisher : PHI Learning Pvt. Ltd.
Release : 2012-01-18
ISBN : 8120345452
Language : En, Es, Fr & De

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Book Description :

This concise introduction to Numerical Methods blends the traditional algebraic approach with the computer-based approach, with special emphasis on evolving algorithms which have been directly transformed into programs in C++. Each numerical method used for solving nonlinear algebraic equations, simultaneous linear equations, differentiation, integration, ordinary differential equations, curve-fitting, etc. is accompanied by an algorithm and the corresponding computer program. All computer programs have been test run on Linux ‘Ubuntu C++’ as well as Window-based ‘Dev C++’, Visual C++ and ‘Turbo C++’ compiler systems. Since different types of C++ compilers are in use today, instructions have been given with each computer program to run it on any kind of compiler. To this effect, an introductory chapter on C++ compilers has been added for ready reference by the students and teachers. Another major feature of the book is the coverage of the practicals prescribed for laboratory work in Numerical Analysis. Each chapter has a large number of laboratory tested programming examples and exercises including questions from previous years’ examinations. This textbook is intended for the undergraduate science students pursuing courses in BSc (Hons.) Physics, BSc (Hons.) Electronics and BSc (Hons.) Mathematics. It is also suitable for courses on Numerical Analysis prescribed for the engineering students of all disciplines.