Elementary Numerical Analysis

Book Description

Offering a clear, precise, and accessible presentation, complete with MATLAB programs, this new Third Edition of Elementary Numerical Analysis gives students the support they need to master basic numerical analysis and scientific computing. Now updated and revised, this significant revision features reorganized and rewritten content, as well as some new additional examples and problems.
The text introduces core areas of numerical analysis and scientific computing along with basic themes of numerical analysis such as the approximation of problems by simpler methods, the construction of algorithms, iteration methods, error analysis, stability, asymptotic error formulas, and the effects of machine arithmetic.

Customer Reviews:

Average Elementary Numerical Analysis Text.......2007-07-10

Just so you know the source of this review and whether or not you should bother trusting me (hmm..maybe not?):
Ph.D. student in Statistics at Iowa State University.
B.S. Computer Science
B.A. Mathematics

Research areas: numerical analysis, analysis of large data sets, stochastic processes
Former research areas: truth maintenance systems, microarray analysis, parallel computing

Note: Not a plug. I like my job.

First off, the book's title is very appropriate. It requires extensive knowledge of calculus and linear algebra, but it uses a fairly non-rigorous "easy" approach to numerical analysis. It's not advanced enough for use in a graduate level class, even for non-majors, but it is very useful and appropriate for sophomore/junior undergraduates. Even though the approach is somewhat non-rigorous, the book doesn't avoid proofs, and though a more advanced mathematician or computer scientist would see holes, it's a book that surely feels complete to most undergraduate math/cs majors/minors.

The explanations and proofs are definitely not perfect. The proofs leave out steps that they assume readers should find obvious. Academic types like Atkinson who have spent years of research in this field often forget just how difficult these concepts are to undergraduates, so some of these "obvious" steps are not going to be obvious to all readers and should not have been omitted. Mixed in with the proofs are some straightforward explanations, but often they are not in layman's terms and I remember scratching my head at times. So I would give the explanations and proofs a C-/D+.

The author does a better job at the exercises. This is a difficult topic, so you don't want to have to work out problems that are too difficult, but some challenge is required to attain mastery of the subject. I think that this book accomplishes that goal. The problems are rarely overly difficult, and though most would be trivial to professors or professionals, they provide enough challenge to undergraduates who are new to the field. The author also does a good job at choosing problems which are relevant. This is nice since many (most, actually) mathematics books include many problems which look contrived and whose results seem meaningless. Anyways, I give the exercises an A.

The content is decent, but a LOT is left out. Traditionally, a two-semester sequence includes a class on numerical analysis as it relates to differential equations and a class on numerical analysis as it relates to linear algebra. Preceding discussion of either one of these topics is a necessary discussion of general iterative methods and analysis of computational error. This book covers all of those topics but none of them extensively. For a one-semester overview, the content is perfect and includes more than enough material. For a traditional two-semester sequence, this book is a bit skimpy. As stated before, the book is also not appropriate for graduate level classes. So if you haven't learned functional analysis, then don't worry--this book is for you. I give the content a B-/C+.

I was a bit disappointed with the computing examples. The examples were not poorly chosen, but there were not enough of them. Also, I think that they should have used a programming language which is easy to read even if you don't know the language. I give the computing examples a D+.

Even though I said that this book is inappropriate for graduate classes, it might serve as a nice reference for graduate students. I always skim through it as a review before certain classes. Though it can be nice as a refresher, a graduate student would probably be happier with something more rigorous like Peter Linz's "Theoretical Numerical Analysis: An Introduction to Advanced Techniques" (overview - very short) or Kendall Atkinson's (the author who wrote this book) "Theoretical Numerical Analysis: A Functional Analysis Framework".

Final note: To those who complain that it requires extensive knowledge of calculus, was that not a prerequisite at your school? The calculus required to understand this book and work the problems is not at a high school level, but it's nothing that a student who has passed college univariate and multivariate calculus shouldn't be able to handle.

2.5 stars

will need supplimentation.......2004-09-16

Of course this book assumes (advanced?) knowledge of Calc 1 & 2 as well as linear algebra and preferably Dif. EQ. These are all prerequisites for the course in which the book is used. That being said, it is quite annoying when the book *completely* skips over intermediate steps involving calculus leaving the student scratching his head. I find myself with my nose more in my Calc. books trying to figure out what the steps leading to the answer rather than learning Num. Analysis. Would have been nice if at least some intermediate steps were added to most problems, but hey, this is college and hand holding should not be assumed.

There are 3 main gripes which contribute to the low rating.

1. The Cost. For the price of the book, (considering the way the material is presented (see 2.) there should be a solution manual bundled with it. (see 3.)

2. The explanations of the material is cut and dry and not verbose at all, [which adds 2 stars to an original 0 rating] however, there is usually only one example for a topic, followed by 10-15 excercises associated with that topic. This often leads to pure frustration and having to "google" for supplimentary material to help me through the problems due to the fact that the example is far more elemantary than the excercises.

3. Lack of solutions. Coupled with the lack of GOOD examples is the lack of solutions for the excercises you just struggled to drudge through. Chapters that typically have 10-15 problems, some with sub-problems in them usually have 5 or so solutions in the back. (so if there is say question 1, parts a-h, question 2, question 3 a - k....there would be a solution for question 1 part c, question 3 part g...).

If you take this course and this is the required text, pray that your professor has great lectures and notes(neither of which my prof. has) or be prepared to spend many hours on google looking for other references.

Maybe i'm just biased..........2002-01-29

I'm biased because i had the good fortune to take Intro to Numeric Analysis from Ken Atkinson himself. I beta-tested this edition of the text, so my copy is in a loose-leaf binder.

Some reviewers have complained that the book is difficult because examples are in FORTRAN rather than C. I disagree. The real meat of the book is written in mathematical form; what source he provides is merely a convenience. When i took his class, most of the students (myself included) implemented in C rather than FORTRAN. No problem, because he was looking for correct results, not reviewing code.

And yes, this book assumes a solid knowledge of calculus, linear algebra, basic differential equations, and discrete logic. Did you think you'd be able to code mathematics without *understanding* it? If you understand the math in the first place, his implementations are very clear. If you don't understand the math, no amount of clarity will save you.

The real beauty, for me, was how he logically built a progression of topics, with each step providing the foundation for the next one. It was like seeing two years of college math in miniature.

it makes numeric sense.......2001-05-09

i had the pain to use this book for my undergrad. coursework for a 200 level class at Cal Poly. Contrary to the other reviewers, i believe the exercises are mediocre, and the material presented lack depth to provide a solid grounding to numerical analysis. Codes are inconveniently written in fortran-97? instead of the more readable pseudo-code. It may provide a good application supplementary for engineering students, but i strongly advise against it for mathematics undergrads. No fun. Lots of handwaving and smoking mirrors.

A strict NO for starters.......2001-04-22

The author presumes that the reader has an advanced knowledge of calculus even though the book is intended for use by undergrads.the content in the chapters of the book are not enough to solve the questions at the end of ech chapter.if you are looking for an introductory course in NA dont even think of using this book.

Numerical Methods for Least Squares Problems

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Numerical Methods for Least Squares Problems
Ake Bjõrck
Manufacturer: SIAM: Society for Industrial and Applied Mathematics
ProductGroup: Book
Binding: Paperback

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ASIN: 0898713609

Book Description

The method of least squares was discovered by Gauss in 1795 and has since become the principal tool for reducing the influence of errors when fitting models to given observations. Today, applications of least squares arise in a great number of scientific areas, such as statistics, geodetics, signal processing, and control. In the last 20 years there has been a great increase in the capacity for automatic data capturing and computing and tremendous progress has been made in numerical methods for least squares problems. Until now there has not been a monograph that covers the full spectrum of relevant problems and methods in least squares. This volume gives an in-depth treatment of topics such as methods for sparse least squares problems, iterative methods, modified least squares, weighted problems, and constrained and regularized problems. The more than 800 references provide a comprehensive survey of the available literature on the subject.

Elementary Stability and Bifurcation Theory (Undergraduate Texts in Mathematics)

Average customer rating:

A Good Presentation For the More Advanced Student
Good but requires that you keep paper and pencil at hand.

Elementary Stability and Bifurcation Theory (Undergraduate Texts in Mathematics)
Gerard Iooss , and Daniel D. Joseph
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0387970681

Book Description

This second edition has been substantially revised. Its purpose is to teach the theory of bifurcation of asymptotic solutions of evolution problems governed by nonlinear differential equations. It is written not only for mathematicians, but for the broadest audience of potentially interested learners, including engineers, biologists, chemists, physicists and economists. For this reason, it uses only well-known methods of classical analysis at a foundation level. Applications and examples are stressed throughout, and these were chosen to be as varied as possible.

Customer Reviews:

A Good Presentation For the More Advanced Student.......2003-12-10

I have used Iooss and Joseph for over 20 years now, starting with the first edition back in the early 80s.

The book is for the more advanced student, one who has a bacic working knowledge of real and functional analysis. Unfortunately, these days, few engineering and physical science students have such a background. Hence, the book would be better if it contained some supporting basic material on mathematical analysis.

The first edition contained numerous "typos". While much improved, the second edition still contains too many "typo" errors.

Overall, the book is a good source of information that should be consulted by anyone interested in bifurcation theory. The book contains material (like the bifurcation of forced T-periodic solutions) not normally included in an elementary treatment of bifurcations.

John Stensby, Professor
Electrical and Computer Engineering
University of Alabama in Huntsville
Huntsville, AL

Good but requires that you keep paper and pencil at hand........1999-09-08

This is an exellent book on stability and bifurcation theory, from an applied math perspective. A reader could just skim and pick up a broad outline but would be better off working though at least some of the messy details to make sure that (s)he is really following the thread of the argument.

Solving Systems of Polynomial Equations (Cbms Regional Conference Series in Mathematics)

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Solving Systems of Polynomial Equations (Cbms Regional Conference Series in Mathematics)
Bernd Sturmfels
Manufacturer: American Mathematical Society
ProductGroup: Book
Binding: Paperback

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ASIN: 0821832514

Book Description

A classic problem in mathematics is solving systems of polynomial equations in several unknowns. Today, polynomial models are ubiquitous and widely used across the sciences. They arise in robotics, coding theory, optimization, mathematical biology, computer vision, game theory, statistics, and numerous other areas.

This book furnishes a bridge across mathematical disciplines and exposes many facets of systems of polynomial equations. It covers a wide spectrum of mathematical techniques and algorithms, both symbolic and numerical.

The set of solutions to a system of polynomial equations is an algebraic variety--the basic object of algebraic geometry. The algorithmic study of algebraic varieties is the central theme of computational algebraic geometry. Exciting recent developments in computer software for geometric calculations have revolutionized the field. Formerly inaccessible problems are now tractable, providing fertile ground for experimentation and conjecture.

The first half of the book gives a snapshot of the state of the art of the topic. Familiar themes are covered in the first five chapters, including polynomials in one variable, Gröbner bases of zero-dimensional ideals, Newton polytopes and Bernstein's Theorem, multidimensional resultants, and primary decomposition.

The second half of the book explores polynomial equations from a variety of novel and unexpected angles. It introduces interdisciplinary connections, discusses highlights of current research, and outlines possible future algorithms. Topics include computation of Nash equilibria in game theory, semidefinite programming and the real Nullstellensatz, the algebraic geometry of statistical models, the piecewise-linear geometry of valuations and amoebas, and the Ehrenpreis-Palamodov theorem on linear partial differential equations with constant coefficients.

Throughout the text, there are many hands-on examples and exercises, including short but complete sessions in Maple®, MATLAB®, Macaulay 2, Singular, PHCpack, CoCoA, and SOSTools. These examples will be particularly useful for readers with no background in algebraic geometry or commutative algebra. Within minutes, readers can learn how to type in polynomial equations and actually see some meaningful results on their computer screens.

Book Description

The subject of sparse matrices has its roots in such diverse fields as management science, power systems analysis, surveying, circuit theory, and structural analysis. Mathematical models in all these areas give rise to very large systems of linear equations which could not be solved were it not for the fact that the matrices contain relatively few non-zero entries. Only comparatively recently, in the last fifteen years or so, has it become apparent that the equations can be solved even when the pattern is irregular, and it is primarily the solution of such problems that is considered in this book. The subject is intensely practical and this book is written with practicalities ever in mind. Whenever two methods are applicable, their rival merits are considered, and conclusions are based on practical experience where theoretical comparison is not possible. Non-numeric computing techniques have been included, as well as frequent illustrations, in an attempt to bridge the usually wide gap between the printed page and the working computer code. Despite this practical bias, it is recognized that many aspects of the subject are of interest in their own right, and the book aims to be suitable also for a student course, probably at M.Sc. level. Exercises have been included to illustrate and strengthen understanding of the material, as well as to extend it. Efficient use of sparsity is a key to solving large problems in many fields. This book will supply both insight and answers for those attempting to solve these problems.

Customer Reviews:

excellent book.......2004-01-31

This book covers direct sparse matrix techniques developed
up to 1986. It's slightly outdated, since this field
experienced great changes -- especially in the early and
mid 90s a lot of new methods were developed.

Book Description

Computing all the zeros of an analytic function and their respective multiplicities, locating clusters of zeros and analytic fuctions, computing zeros and poles of meromorphic functions, and solving systems of analytic equations are problems in computational complex analysis that lead to a rich blend of mathematics and numerical analysis. This book treats these four problems in a unified way. It contains not only theoretical results (based on formal orthogonal polynomials or rational interpolation) but also numerical analysis and algorithmic aspects, implementation heuristics, and polished software (the package ZEAL) that is available via the CPC Program Library. Graduate studets and researchers in numerical mathematics will find this book very readable.

Elementary Theory and Application of Numerical Analysis

Average customer rating:

This is a nice little start to numerical analysis

Elementary Theory and Application of Numerical Analysis
David G. Moursund , and Charles S. Duris
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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ASIN: 048665754X

Book Description

Concise, rigorous introduction to modern numerical analysis, especially error-analysis aspects of problems and algorithms discussed. Aimed primarily at sophomore- and junior-level engineering and physical sciences majors, book focuses on a small number of basic concepts and techniques, emphasizing why each works. Exercises and answers.

Customer Reviews:

This is a nice little start to numerical analysis.......2001-06-07

This is a nice little start to numerical analysis. None of the underlying real variable theory is explored in the detail. Basically, an undergraduate exposure to calculus and linear algebra is all that is required. The basic topics are covered such as integration, numerical differentiation, and interpolation. There are numerous worked out examples and the text is sprinkled with snippets of Fortran code. However, all of the material covered here is contained in Press' "Numerical Recipes in C" .

Methods for Solving Systems of Nonlinear Equations (CBMS-NSF Regional Conference Series in Applied Mathematics)

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Methods for Solving Systems of Nonlinear Equations (CBMS-NSF Regional Conference Series in Applied Mathematics)
Werner C. Rheinboldt
Manufacturer: Society for Industrial Mathematics
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Binding: Paperback

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ASIN: 089871415X

Book Description

This second edition provides much-needed updates to the original volume. Like the first edition, it emphasizes the ideas behind the algorithms as well as their theoretical foundations and properties, rather than focusing strictly on computational details; at the same time, this new version is now largely self-contained and includes essential proofs. Additions have been made to almost every chapter, including an introduction to the theory of inexact Newton methods, a basic theory of continuation methods in the setting of differentiable manifolds, and an expanded discussion of minimization methods. New information on parametrized equations and continuation incorporates research since the first edition.

Elementary Numerical Analysis: An Algorithmic Approach

Average customer rating:

It is a good book but does needs for examples

Elementary Numerical Analysis: An Algorithmic Approach
Samuel Daniel Conte
Manufacturer: McGraw-Hill Companies
ProductGroup: Book
Binding: Hardcover

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ASIN: 0070124477

Customer Reviews:

It is a good book but does needs for examples.......1998-10-20

The book should have more examples per topic, one example is not enough for a difficult subject like Numerical Analysis. The book does not provide the answers for the exercises and students do not have a way to check if they are doing the exercises correctly.

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