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A classic
Table of contents

1. SOME BASIC IDENTITIES AND INEQUALITIES
1.0 Objectives; Notation
1.1 Elementary Matrices
1.2 Some Factorizations
1.3 Projections, and the General Reciprocal
1.4 Some Determinantal Identities
1.5 Lanczos Algorithm for Tridiagonalization
1.6 Orthogonal Polynomials
References
Problems and Exercises

2. NORMS, BOUNDS, AND CONVERGENCE
2.0 The Notion of a Norm
2.1 Convex Sets and Convex Bodies
2.2 Norms and Bounds
2.3 Norms, Bounds, and Spectral Radii
2.4 Nonnegative Matrices
2.5 Convergence; Functions of Matrices
References
Problems and Exercises

3. LOCALIZATION THEOREMS AND OTHER INEQUALITIES
3.0 Basic Definitions
3.1 Exclusion Theorems
3.2 Inclusion and Separation Theorems
3.3 Minimax Theorems and the Field of Values
3.4 Inequalities of Wielandt Kantorovich
References
Problems and Exercises

4. THE SOLUTION OF LINEAR SYSTEMS: METHODS OF SUCCESSIVE APPROXIMATION
4.0 Direct Methods and Others
4.1 The Inversion of Matrices
4.2 Methods of Projection
4.3 Norm-Reducing Methods
References
Problems and Exercises

5. DIRECT METHODS OF INVERSION
5.0 Uses of the Inverse
5.1 The Method of Modification
5.2 Triangularization
5.3 A More General Formulation
5.4 Orthogonal Triangularization
5.5 Orthogonalization
5.6 Orthogonalization and Projection
5.7 The Method of Conjugate Gradients
References
Problems and Exercises

6. PROPER VALUES AND VECTORS: NORMALIZATION AND REDUCTION OF THE MATRIX
6.0 Purpose of Normalization
6.1 The Method of Krylov
6.2 The Weber-Voetter Method
6.3 The Method of Danilevskii
6.4 The Hessenberg and the Lanczos Reductions
6.5 Proper Values and Vectors
6.6 The Method of Samuelson and Bryan
6.7 The Method of Leverrier
References
Problems and Exercises

7.PROPER VALUES AND VECTORS: SUCCESSIVE APPROXIMATION
7.0 Methods of Successive Approximation
7.1 The Method of Jacobi
7.2 The Method of Collar and Jahn
7.3 Powers of a Matrix
7.4 Simple Iteration (the Power Method)
7.5 Multiple Roots and Principal Vectors
7.6 Staircase Iteration (Treppeniteration)
7.7 The LR-Transformation
7.8 Bi-iteration
7.9 The QR-Transformation
References
Problems and Exercises

BIBLIOGRAPHY
INDEX ... Read more

Product Description
The term "Numerical Analysis," in this text, means the branch of mathematics that develops and analyzes computational methods dealing with problems arising in classical analysis, approximation theory, the theory of equations, and ordinary differential equations. The topics included in the book are presented with a view toward stressing basic principles and maintaining simplicity and teachability as far as possible. In this sense, the text is an introduction. Topics that, even though important, require a level of technicality that goes beyond the standards of simplicity imposed, are referenced in detailed bibliographic notes at the end of each chapter. In this way, the reader is given guidance and an opportunity to pursue advanced modern topics in more depth.

Contrary to tradition, the text does not include numerical linear algebra, which is felt by the author to have matured into an autonomous discipline having an identity of its own and therefore deserving treatment in separate books and separate courses on the graduate level. For similar reasons, the numerical solution of partial differential equations is not covered either.

The text is geared to a one- or two-semester graduate course in numerical analysis for students who have a good background in calculus and advanced calculus and some knowledge of linear algebra, complex analysis, and differential equations. Previous exposure tonumerical methods in an undergraduate course is desirable but not absolutely necessary.

A significant feature of the book is a large collection of exercises, both the kind that deal with theoretical and practical aspects of the subject and those requiring machine computation and the use of mathematical software. ... Read more

Customer Reviews (1)

This is Numerical Analysis
When I was taking a class in numerical analysis, I got the required text, but found I ended up reading this book instead.There's a lot more that connects with what numerical analysis is, in an abstract sense, than most other texts I've seen on the subject (most of which focus on a more computational almost plug and chug application instead of the theoretical underpinnings).Moreover, the subject seemed to flow continuously from one subject to another and there were plenty of exercises.

As a criticism, I don't appreciate the verbose layout, but in the end it might have been necessary. ... Read more

Product Description
"Substantial, detailed and rigorous ... readers for whom the book is intended are admirably served."--MathSciNet (Mathematical Reviews on the Web), American Mathematical Society.Practical text strikes fine balance between students' requirements for theoretical treatment and needs of practitioners, with best methods for large- and small-scale computing. Prerequisites are minimal (calculus, linear algebra, and preferably some acquaintance with computer programming). Text includes many worked examples, problems, and an extensive bibliography. 1974 ed.
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Customer Reviews (2)

superfast
The book arrived at the time one day before I hoped.
The book was also clean enough.
The seller is deserved to 5+ stars.

Classic piece in numerical analysis.
This is a classic piece in numerical analysis.
The book is normally very hard to get hand on.
The sections on discretization schemes and
ODEs are excellent.
Not an in-depth book but an overview book.
Does not cover late developments.
Dahlquist has made significant and well
known contributions to ODE solver theory.
The origin is the department for numerical analysis
at the Royal Institute of Technology in Stockholm,
Sweden ...
A second edition is reportedly under way. ... Read more

Product Description

Differential geometry techniques have very useful and important applications in partial differential equations and quantum mechanics. This work presents a purely geometric treatment of problems in physics involving quantum harmonic oscillators, quartic oscillators, minimal surfaces, Schrödinger's, Einstein's and Newton's equations, and others. Historically, problems in these areas were approached using the Fourier transform or path integrals, although in some cases, e.g., the case of quartic oscillators, these methods do not work. New geometric methods, which have the advantage of providing quantitative or at least qualitative descriptions of operators, many of which cannot be treated by other methods, are introduced. And, conservation laws of the Euler--Lagrange equations are employed to solve the equations of motion qualitatively when quantitative analysis is not possible.

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Product Description
This text emphasizes the intelligent application of approximation techniques to the type of problems that commonly occur in engineering and the physical sciences. Students learn why the numerical methods work, what type of errors to expect, and when an application might lead to difficulties. The authors also provide information about the availability of high-quality software for numerical approximation routines. The techniques are essentially the same as those covered in the authors' top-selling Numerical Analysis text, but in this text, full mathematical justifications are provided only if they are concise and add to the understanding of the methods. The emphasis is placed on describing each technique from an implementation standpoint, and on convincing the student that the method is reasonable both mathematically and computationally. ... Read more

Customer Reviews (3)

Saved me $140!!
Thanks so much for this book. At my local bookstore I would have had to pay $180. I went online and found a NEW copy for $40 - saving me almost $140. The book is fine, I use it as a textbook for class, and it is very easy to follow.

Almost good enough to make me switch
In my never-ending quest for the best textbook for each of my courses, I examine a large number of math and computer books. The current book used in my numerical analysis class is "Elementary Numerical Analysis" by Atkinson and Han. My standard criterion for changing is that the new book must be significantly better than my current favorite. By significantly better, I mean that the cost to me when changing is more than offset by the advantages that the new book gives the students.
While I consider this book on a par with the Atkinson book and maybe even a bit better, it doesn't quite cross the threshold. The coverage is what is ordinarily considered that of a one-semester course in numerical analysis, so in that regard it is still in the pack. A broad spectrum of exercises appears at the ends of the sections and solutions to the odd-numbered ones appear in an appendix.
I consider this book to be slightly more readable than some of the others that I have seen. Maple is used as the symbolic mathematics package used to illustrate the examples and a CD containing the code used to generate the examples is included. This book is good enough to tempt me to make the switch but not good enough to make me do it.

Good book for Numerical Methods Class
I had previously sat in on a Numerical Analysis class, and I have to say that this book was much better than the one that we were forced to use.The examples were clear, and the text focused much less on proofs and more on how to do problems and calculate their error.The sample programs on disk were also thorough, and included in several different languages (c, fortran, pascal, maple, mathematica, & matlab). ... Read more

Product Description
This book provides maximum teaching flexibility by beginning each chapter and each section with basic, elementary material, and gradually builds up to more advanced material. It continues this flexibility with its approach to computing languages - the book is not specific to any one computing language. It emphasizes a "cause and effect" approach to numerical mathematics.
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Customer Reviews (2)

very well written, but missing important topics
I would give this book 4 stars, but I had to give it 3 stars to counter the earlier review, which seems to be very skewed.

For the topics that are covered in the book, this book is extremely well written and readable, and it balances practical and theoretical aspects very well. This is not typical for numerical analysis books! Unfortunately, this book lacks some important topics that should be in an introductory textbook. For example, optimization is so important and ubiquitous in numerical computations, and it is no more advanced than eigenvalue problems and PDEs, so it is surprising to me the subject is not even mentioned in the book. Also the book does not have a section on numerical differentiation, but instead scattered it into sections 2.2 and 6.10.1 without introducing the concepts and terminology properly. These deficiencies make the book ill-suited as a primary textbook or a reference book. Heath's Scientific Computing book is at about the same level of exposure as this book and is equally well written, while being far more comprehensive.

What does it mean?
I found this text book to be well thought out and presented in a mannor that I could digest more easily.I actually enjoyed (as much as a person can) working these problems.At the end of the semester I had really used this text book and my understading of more advanced math concepts had reached a new level.

... Read more

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Young Madison spends a typical day visiting with friends and family; follow along to see how she is learning ever step of the way! This book invites readers to explore the world of learning through the eyes of a child. Find out how children learn in a variety of different ways as they explore all that is around them. Discover how learning can occur while baking cookies or while jumping rope with friends.

Product Description
This highly successful and scholarly book introduces students with diverse backgrounds to the 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 careful proofs and scientific background.An in-depth treatment of the topics of numerical analysis, a more scholarly approach, and a different menu of topics sets this book apart from the authors' well-respected and best-selling text: NUMERICAL MATHEMATICS AND COMPUTING, FOURTH EDITION. ... Read more

Customer Reviews (7)

Good book
Bought this as a textbook for my class. The book is pretty well-organized and easy to read. I like it. I was reading some other books of Numerical Analysis, and they are pretty old, maybe that's why they are less organized than this one.

Are You Just Taking a Class?
If you are a graduate student then this book might appeal to you.But if you are actually trying to use the book for some purposeful end, it will probably disappoint.

The first problem is that it uses lots and lots of mathematical symbols, as well as plenty of abstruse matrix transformations.If you are studying for your PhD then you probably will have no trouble.

The next problem is that the book is pretty much page after page of solid proofs.The proofs are essentially meaningless; they are presented without context and are rarely used for anything except building other proofs.In the places where numerical examples are presented, they are so brief and cryptic as to be unintelligible.

Believe it or not, the same authors wrote another book, Numerical Mathematics and Computing - it covers almost exactly the same material, but in a more down-to-earth way.If you are determined to read Numerical Analysis, then I would highly recommend that you read the other book first.Instead of having copious proofs, the other book spends its time reviewing the mathematical methods required to apply the material, as well as reviewing the notation.

A higher level of rigor than found in most numerical methods texts
I teach a course in numerical methods every other year and use Maple as the platform for the computer solution of problems. At this time, I am using "Numerical Methods: Third edition" by Faires and Burden and am quite happy with it. However, I am always trolling for better textbooks so that it is premise with which I examined this book.
The level of rigor is on the higher end of the scale, there are many more formal theorems and proofs than is found in most of the other numerical methods textbooks. Rather than using code in Maple or Mathematica, the algorithms are expressed in a lower level pseudocode.It has the appearance of a programming language; however some of the operations are expressed in mathematical form for brevity. This use of the mathematical syntax generally makes them easier to understand than if they were expanded out using a programming language. There are many exercises at the end of the sections, including a group meant for computer solution.
I will not be adopting this book for my class, the level of rigor is a bit higher than my students can easily digest and quite frankly, I am hooked on using Maple as the computer platform. Nevertheless, it serves as a valuable secondary reference, where when necessary, I can look through a detailed proof of a topic that I am about to present.

Horrible Book.
Honestly, this has turned out to be a horrible book. Particularly in the disconnect that exists between the text and the problem sets.Very few of the examples are useful to read through because they are trivially simple, while the problem sets seem to take particular delight in finding the hardest tricks to be solve-able.

I would highly suggest that anyone that purchases this book, already know what they are trying to learn,or have an excellent teacher that can fill in the gaps.

Book for the U
I bought this book for my college and it was excellent ... Read more

Product Description
Exploring Numerical Methods: An Introduction to Scientific Computing stresses insight and hands-on experience as it provides students in mathematics, engineering, computer science, and the physical sciences a well-crafted introduction to traditional numerical analysis topics. The text includes an exploration section with problems that deal with the practical issues of software evaluation, selection, modification, and solutions to not-entirely-open-ended problems. Designed to accommodate the needs of beginner and more experienced students, the text encourages active learning, and uses MATLAB to implement the methods and algorithms that it discusses. Students are provided with a strong experiential foundation for future study. ... Read more

Product 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. ... Read more

Customer Reviews (2)

Good book with a good professor
This book is good at explaining some of the theorem involves and derivation of the algorithm/pseudo-codes. However, it makes certain assumption that should not be make lightly. Some of the problems indicated the matrix is using the concept of principle minor. If the reader did not read the section, they will not see the part where the book indicated to treat principle minor as leading principle minor. Since the two concepts are not the same, the book could be confusing to those that understand the concept and just want to practice the question, or simply scan the text before trying out the questions. The book also assume the reader have extensive knowledge of linear algebra. Therefore, this book is not for reader with basic linear algebra concept.

Edit: I have even more trouble reading this book than any other textbook I encounter. The concept of Aitken Acceleration was not clear on how it is used in the algorithm. It seems like the idea was inserted in between power method and inverse power method. There was no noticeable use of the Aitken Acceleration in the inverse power method where you would assume some relation to the theorem just mentioned. Really not for a student who is learning all these new concepts.

Great book for understanding the theoretical aspect of the subject
Most of the numerical analysis books for the beginners seem to be very compact. This book on the other hand is more elaborate and explains how all the formulas are derived rather than just stating it. So, if a student wants a clear understanding of the theoretical aspect of the subject rather than just applying it, this book can be a valuable collection. ... Read more

Product Description
This republication addresses some of the basic questions in numerical analysis: convergence theorems for iterative methods for both linear and nonlinear equations; discretization error, especially for ordinary differential equations; rounding error analysis; sensitivity of eigenvalues; and solutions of linear equations with respect to changes in the data. ... Read more

Product Description
This is the first book on constructive methods for, and applications of orthogonal polynomials, and the first available collection of relevant Matlab codes. The book begins with a concise introduction to the theory of polynomials orthogonal on the real line (or a portion thereof), relative to a positive measure of integration. Topics which are particularly relevant to computation are emphasized. The second chapter develops computational methods for generating the coefficients in the basic three-term recurrence relation. The methods are of two kinds: moment-based methods and discretization methods. The former are provided with a detailed sensitivity analysis. Other topics addressed concern Cauchy integrals of orthogonal polynomials and their computation, a new discussion of modification algorithms, and the generation of Sobolev orthogonal polynomials. The final chapter deals with selected applications: the numerical evaluation of integrals, especially by Gauss-type quadrature methods, polynomial least squares approximation, moment-preserving spline approximation, and the summation of slowly convergent series. Detailed historic and bibliographic notes are appended to each chapter. The book will be of interest not only to mathematicians and numerical analysts, but also to a wide clientele of scientists and engineers who perceive a need for applying orthogonal polynomials. ... Read more

Product Description
This book provides a fundamental introduction to numerical analysis.This book covers numerous topics including Interpolation and Polynomial Approximation,Curve Fitting, Numerical Differentiation, Numerical Integration, and Numerical Optimization. For engineering and computer science fields. ... Read more

Customer Reviews (7)

Very good shape
This book is in near perfect condition and so far has been fairly helpful in my course.

Numerical Methods Using MATLAB
This is an excellent product. It came in great timing. I recommend seller to everyone in need of this product.

Satisfactory, but with flaws
The Math Part:
I have to use this as the main text for a college math class, and while it may be a good reference book or engineering text, I don't think it's the best choice for a math course. It's written in such a way that you can flip to the section/topic you need and immediately get the main points and the formulas. But the authors don't necessarily teach their materials in the most intuitive way and frankly, don't seem that concerned with intuition at all. This makes the book quite sufficient as reference for your computations in your bioinformatics research project and such, but for a math text I would be more interested in really owning the intuition and tricky ideas so I can generalize to new cases or derive the formulas, rather than discovering 20 gazillion technical details/equations that will magically spew out an answer for who knows what reason. See the bajillion formulas on cubic splines for what I mean. Or see how instead of simple example + intuition, the authors chose to do 20 pages demonstrating Gaussian elimination.

The Matlab Part:
I learned Matlab in a few weeks from "Mastering MATLAB 7" and playing around with it on my own. It's very easy to just use the built-in manual or find all kinds of solutions to common problems using Google. There's really nothing wrong or tedious with picking up Matlab knowledge "from the manuals, man pages, the Internet, etc..." as one reviewer complained, because a language is necessarily something you pick up gradually and continually. Personally I think the reviewer was misleading in implying that this book does a good job teaching beginners Matlab. There's 1-2 programs per section, and no explanations in terms of the programming. Honestly, what are the chances that these programs will just drop into your lap and fit perfectly whatever application it is that you presumably need these numerical methods for? You will need to tailor the programs to your objectives or at least, understand WHY and HOW they work, in order to really take advantage of them, and that is outside the scope of this book. What this book really offers are the algorithms behind the programs, and not the programs themselves that are useful. In my opinion the Matlab programs were just a selling point, that's all.

There were also lots of little things that I personally just did not like about the book, where I felt the authors cut corners in their explanations or didn't phrase certain things in the best ways or used slightly funky notation or were not organized enough. Not a great math book in my opinion. But objectively speaking most people probably don't mind those kinds of details and aren't necessarily looking for a math book. So with that in mind I give it a 4.

A decent textbook without unnecessary clutter
This book goes straight to the heart of the numerical methods without unnecessary distracting fancy pictures and layout that some numerical methods textbook for engineers have. Also, the book has enough Matlab programs for a reader/student to understand essentials of Matlab programming and then tweak/modify the programs for further applications.

I wish author incorporates numerical methods for nonlinear ODE boundary value problems and eigenvalue problems related to ODE in the future edition.

Overall, it is an excellent introductory numerical methods textbook for science and engineering students. After grasping the fundamentals in this textbook, student/reader will tend to be more confident and enthusiastic while studying Numerical Analysis.

Much needed book
Whether you are an instructor for an Engineering class, Life Sciences, Statistics, Mathematics, or simply want to add practical mathematical analysis and programming, this book is the book you should use.I have been using Matlab for a number of years, and I had to pick up my Matlab knowledge from the manuals, man pages, the Internet, etc... and finding out the ins and outs of how to do something was not always an easy task nor accurate.Mathews and Fink's book put all you need to know about the most popular Mathematical methods at your finger tips.The book is tailored such that it can be used alone in a Mathematics course, or as reference in an Engineering course.One field of study that has enjoyed the power and flexibility of Matlab in the recent years is Computational Biology or Bioinformatics.Even though there are plenty of applications popping up here and there for this area of research, the area is still very much untapped and algorithms need to be developed for it as we go forward.Matlab is the best way to try out these new or improved algorithms, and use some of the available tools out there to generate C source code from your Matlab files.This method of algorithms development could save you tons of time, since Matlab makes numerical programming very simple.

The authors start with the basics in Numerical Methods; assuming that this book will be used as the primary text book in the course.A very good assumption, and the instructors who choose otherwise, can always skip the preliminaries.The context of text aims to provide a good balance of theory and application.One way that the authors try to keep this balance is to talk about "error" rate for the algorithms in question.The students are thought the limitations of Matlab along with the strengths of the software, and error analysis is one way to show the students that the results of numerical analysis is Matlab is not perfect, and more importantly why.This error analysis is done for every major algorithm and method presented in the text, and a number of methodologies are presented to help the student in figuring out this rate.

Authors start the main contents of the book with a representation of basic Linear Systems followed by a more complicated topic of Polynomial Approximation.Taylor Series and Lagrange Approximations are thoroughly covered in theory followed by examples that are solved by "hand" and by Matlab.The examples are complete, and can even be used, at least to start with, for the problem sets at the end of the chapter.As one would guess, curve fitting is the next topic of discussion.As you know, numerical techniques in science and engineering often requires curve fitting of experimental data.Starting with simple techniques of Least-Squares Lines, non-Linear Least-Square Methods and ending with the four different flavors of Spline Functions.The Matlab examples becomes more advanced as the topic progresses, and more and more examples are given as the topics get more complicated as well.

One can not learn Numerical Methods without a deep understanding of Numerical Differentiation and Numerical Integrations.Numerical methods for Differentiation are used to solve boundary value problems in ordinary differential equations and partial differential equations.Heat Transfer, Semiconductor Physics and Device Modeling, an Physical modeling of Molecules are just some of the examples that use these numerical differentiation techniques to solve problems.As is the case with the book, the authors start talking the theory behind how numerical differentiation works, and then, they go into the Matlab representation of the problem.Various approximation methods are presented, and error rate for each approximation method is also calculated in detail - both by hand and using Matlab.
Numerical Integration is a bit more difficult, as there are a number of ways to calculate the area under a curve.The authors present four numerical methods in detail: quadrature, composite trapezoidal, adaptive quadrature and Gauss-Legendre Integration.Each theory is followed by an example Matlab programs.The authors wrap up the text by talking about differential equations and partials differential equations.These two topics are difficult without using numerical methods, and it is even harder to follow the numerical theory of these topics.The authors take a slightly different approach to these topics.They start with examples from the get go.Instead of laying down the theory, they start each chapter with relevant examples from simple to more complex and abstract.Wave Equations and Heat Transfer equations are well known applications of PDE that are presented in detail. Eigenvalues, eigenvectors and the Jacodi's Meothod wrap up this text by j. H. Mathews and K. D. Fink.

I would recommend this book to be used for second year Mathematics, Physical Sciences or Engineering students.A course in Numerical Methods would benefit greatly from this book.Other students can certainly use this text to assist them with modeling, simulation and statistical problems in Electrical Engineering, Mechanical Engineering and various Applied Chemistry and Physics courses.
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Product Description
Textbook bringing together four key elements of numerical analysis with MATLAB: MATLAB programming techniques; the mathematical basis of numerical methods; applications of numerical analysis in engineering; scientific and mathematical problems; and the creation of scientific graphics. Previous edition: c1995. DLC: Computer graphics. ... Read more

Customer Reviews (3)

Excellent
The best INTRODUCTION ever, in numerical analysis. The author has an exquisite pedagogical approach in his presentation.

This book may also be valuable for those interested in advanced notions (often poorly presented)as it gives a practical picture of things prior to tackling further issues.

Great book.

don't waste your money on such a pile of trash
Not clear from the very beginning and not many things you can learn from this book

Numerical Analysis and Graphics Visualization With Matlab
this book waws very helpful in creating maps of pixelated tif images in the optic research I conduct at LSUMC ... Read more