Numerical analysis is an increasingly important link between pure mathematics and its application in science and technology. This textbook provides an introduction to the justification and development of constructive methods that provide sufficiently accurate approximations to the solution of numerical problems, and the analysis of the influence that errors in data, finite-precision calculations, and approximation formulas have on results, problem formulation and the choice of method. It also serves as an introduction to scientific programming in MATLAB, including many simple and difficult, theoretical and computational exercises. A unique feature of this book is the consequent development of interval analysis as a tool for rigorous computation and computer assisted proofs, along with the traditional material.
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"The book is well organized and has excellent examples. It represents a very nice addition to the set of numerical analysis texts currently available." Mathematical Reviews
Book Description
Numerical analysis is an increasingly important link between pure mathematics and its application in science and technology. This textbook provides an introduction to the justification and development of constructive methods that provide sufficiently accurate approximations to the solution of numerical problems, and the analysis of the influence that errors in data, finite-precision calculations, and approximation formulas have on results, problem formulation and the choice of method. It also serves as an introduction to scientific programming in MATLAB, including many simple and difficult, theoretical and computational exercises.A unique feature of this book is the consequent development of interval analysis as a tool for rigorous computation and computer assisted proofs, along with the traditional material.
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2 of 2 people found the following review helpful:
4.0 out of 5 stars
more advanced than its title suggests,
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This review is from: Introduction to Numerical Analysis (Paperback)
The author offers this as an introductory book on the subject. Maybe so. But you had better have a solid background in classical analysis. On the level of Marsden's "Elementary Classical Analysis", for example.
Neumaier describes the various numerical methods from a more rigorous standpoint than most other books on numerical analysis. So, for example, you should already be acquainted with such ideas as a closed convex hull or the infinity norm. It is not totally theoretical. He shows the use of Maple for generating results. Though perhaps examples in Mathematica would also be useful. The book is good for those of you who want a detailed treatment of the conceptual foundations of the field.
1 of 1 people found the following review helpful:
4.0 out of 5 stars
Suitable selection for a numerical analysis text, however not as good as the one I use now,
By Charles Ashbacher (Marion, Iowa United States) - See all my reviews (TOP 500 REVIEWER) (VINE VOICE) (HALL OF FAME REVIEWER)
This review is from: Introduction to Numerical Analysis (Paperback)
I teach a course in numerical methods approximately every two years and am always looking for "the ideal textbook." At this time I am using "Elementary Numerical Analysis: Third Edition" by Atkinson and Han. I examined this book to determine if it would be a better selection for the course.
This book covers all of the standard fare for the course: *) Fundamental analysis of computer error *) Solving linear systems of equations *) Interpolation and numerical differentiation *) Numerical integration *) Solving nonlinear equations *) Solving systems of nonlinear equations The quality of the explanations is slightly weaker than in the Atkinson book, there is nothing specific to point to; I just find the Atkinson book more readable. Algorithms in both books are expressed in Matlab code, so there is no real difference there. In conclusion, while I found that this book is certainly usable and may even be ranked as my second choice, at this time I will not be adopting in for use in my course.
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Inside This Book
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First Sentence:
In this chapter, we introduce the reader on a very elementary level to some basic considerations in numerical analysis. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
complete spline interpolant, secant bisection method, definite eigenvalue problems, mean value form, root secant method, triangular factorization, pivot search, regular zero, superlinear convergence, spiral search, interval arithmetic, argument reduction, automatic differentiation, differential numbers, convergence order, finite precision arithmetic, interpolation points, interval evaluation, interpolation polynomial, iterative refinement, limiting accuracy, multistep methods, sum norm, exponent range, pivot element Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof of Theorem, Proof Suppose, Results of Newton New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In this chapter, we introduce the reader on a very elementary level to some basic considerations in numerical analysis. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
complete spline interpolant, secant bisection method, definite eigenvalue problems, mean value form, root secant method, triangular factorization, pivot search, regular zero, superlinear convergence, spiral search, interval arithmetic, argument reduction, automatic differentiation, differential numbers, convergence order, finite precision arithmetic, interpolation points, interval evaluation, interpolation polynomial, iterative refinement, limiting accuracy, multistep methods, sum norm, exponent range, pivot element Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof of Theorem, Proof Suppose, Results of Newton New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 31
books:
See all 31 books this book cites
4
books
cite this book:
- Acta Numerica 2002: Volume 11 by Arieh Iserles in Back Matter (1), and Back Matter (2)
- Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems by Alexander Morgan in Back Matter
- Parameter-Free Iterative Linear Solvers (Mathematical Research) by R?diger Weiss in Back Matter
- Practical Optimization by Philip E. Gill in Back Matter
- Matrix Iterative Analysis (Springer Series in Computational Mathematics) by Richard S. Varga in Back Matter
See all 31 books this book cites
- Acta Numerica 2004: Volume 13 by Arieh Iserles on page 364
- Interval Methods for Systems of Equations (Encyclopedia of Mathematics and its Applications) by A. Neumaier in Back Matter
- Computer Vision - ACCV 2006: 7th Asian Conference on Computer Vision, Hyderabad, India, January 13-16, 2006, Proceedings, Part I (Lecture Notes in ... Pattern Recognition, and Graphics) (Pt. 1) by P.J. Narayanan on page 20
- Global Optimization and Constraint Satisfaction: First International Workshop Global Constraint Optimization and Constraint Satisfaction, COCOS 2002, ... Papers (Lecture Notes in Computer Science) by Christian Bliek on page 70
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