Average customer rating:
- a wide variety of topics
- Very nice introduction
- Short and Sweet
- Much needed desktop reference for anyone working with algorithms, networking protocols, optimization
- Only for graduate level - very good
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Approximation Algorithms
Vijay V. Vazirani
Manufacturer: Springer
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ASIN: 3540653678 |
Book Description
This book covers the dominant theoretical approaches to the approximate solution of hard combinatorial optimization and enumeration problems. It contains elegant combinatorial theory, useful and interesting algorithms, and deep results about the intrinsic complexity of combinatorial problems. Its clarity of exposition and excellent selection of exercises will make it accessible and appealing to all those with a taste for mathematics and algorithms.
Richard Karp,University Professor, University of California at Berkeley
Following the development of basic combinatorial optimization techniques in the 1960s and 1970s, a main open question was to develop a theory of approximation algorithms. In the 1990s, parallel developments in techniques for designing approximation algorithms as well as methods for proving hardness of approximation results have led to a beautiful theory. The need to solve truly large instances of computationally hard problems, such as those arising from the Internet or the human genome project, has also increased interest in this theory. The field is currently very active, with the toolbox of approximation algorithm design techniques getting always richer.
It is a pleasure to recommend Vijay Vazirani's well-written and comprehensive book on this important and timely topic. I am sure the reader will find it most useful both as an introduction to approximability as well as a reference to the many aspects of approximation algorithms.
László Lovász, Senior Researcher, Microsoft Research
Customer Reviews:
a wide variety of topics.......2006-11-07
Vazirani's book seems well suited for a computer science researcher who has had a rigorous background in pure maths. The level of difficulty can be quite advanced. Also, it is not the sort of book that gives algorithm examples in an actual programming language. Not that this should be a handicap to a skilled reader. The algorithms are usually described in high level pseudocode. You have to manually instantiate these in the language of your preference.
The 30 chapters span a wide variety of computational topics. Some are simpler than others to understand. Like the chapter on finding the shortest vector from the integer lattice made from a set of linearly independent vectors. That requires only a year or so of introductory linear algebra.
There are exercises for each chapter. Some exercises are formidable. Essentially like little research problems in their own right. Another plus for the book.
Very nice introduction.......2006-05-20
This is a quite nice book by an author who is well-known in the field. The book is not thematic, instead it presents certain problems in each chapter along with the main approximation algorithms and correctness proofs. Yet, each new concept is well introduced with the problems. For instance, the author presents LP-based techniques on the same problem (set cover) in the second part of the book. This makes it quite easy to compare and understand different techniques. The last part of the book is a little bit advanced compared to the first two parts which uses combinatorial or LP-based analysis of the algorithms. The presentation of the PCP theorem- arguably the deepest theorem of computer science- and its consequences are also in the last part.
A warning though: The book is quite terse at times, which enforces a dense reading. This may not be suitable for an undergradute study. My only complaint is that the PCP theorem might well be introduced with a little more intution.
Overall, I rate this book as excellent. If you are interested in algorithms, you should definitely buy it. Also, buy the "Complexity and Approximation" by Ausiello, Crescenzi and others. They provide a more comprehensive and thematic treatment. It also has an excellent bibliography and list of NP-hard problems. These two will make a great couple. The book edited by Hochbaum (Approximation Algorithms for NP-hard problems) on the other hand presents detailed information on the algorithms.
Short and Sweet.......2006-03-13
This is a fanastic topics book in approximation algorithms. The problems and proofs are challenging and concise, but written in a very accessible manner. It is a great reference book, and also a convenient place to grab a lecture from if you need something to fill our a course. I have found it extremely useful, and even fun to read. I highly reccomend it for any person interested in theoretical computer science.
Much needed desktop reference for anyone working with algorithms, networking protocols, optimization.......2006-03-09
I have been looking for books related to solving NP-complete and NP-hard problems approximately. There is another book by Hochbaum and I have that too. Unfortunately, that book is more of a research oriented book as it is written by several researchers. It's like reading several research papers within two hard covers. This means that one needs to have a sort of intermediate level of experience with approximation algorithms.
For a beginner, one would expect a book that starts from ground-up and that has been written as a textbook rather than as a set of research papers. The book by Dr. Vazirani, is the only book that is written by one author with a step-by-step evolution of concepts and ideas related to approximation algorithms.
Only for graduate level - very good.......2005-11-22
Very good, it is easy to read the book if you have a good level
of knowledge and the experience to think some details in the
proofs of the theorems.
I think it is a very good book for a graduate student.
Book Description
The second, revised edition of this book covers all aspects of non-uniform rational B-splines necessary to design geometry in a computer-aided environment. Basic B-spline features, curve and surface algorithms, and state-of-the-art geometry tools are all discussed. Detailed code for design algorithms and computational tricks are covered, too, in a lucid, easy-to-understand style, with a minimum of mathematics and using numerous worked examples. The book is a must for students, researchers, and implementors whose work involves the use of splines.
Customer Reviews:
Good reference for implementers who are familiar with NURBS.......2003-07-24
This book is best for those who have at least become familiar with Bezier and NURBS curves and surfaces and want to start implementing some programs.
The illustrations are not as clear as they could be so it may make it a little difficult for first-timers to understand. If you're unfamiliar with Bezier and NURBS curves then "Curves and Surfaces for CAGD" by Farin is probably a better place to start. But if you get Farin's book make sure to get the 5th edition since earlier editions aren't as clear.
With that said there is a wealth of information about creating and manipulating NURBS geometry in this book. All explanations are followed by code implementation. The code is a little difficult to understand at first, but if you stick with it you'll understand their coding style.
4 stars since thier layout and illustrations could be a lot clearer.
An Essential Foundation.......2002-08-07
I own many books on the subject of NURBS. I always come back to this one while programming NURBS and reading research papers. It provides a fantastic foundation. It is an older book, so don't expect recent research to be included. For those that also want to know how to do ray tracing with NURBS surfaces look here:
...
Good luck!
This is a definitely a math book, not a programming book !.......2000-05-23
This book is complete, but there is too many math formula. The composition is appr. 80% formula explanation, 10% sample and 10% algorithm. So if you are a programmer you are wasting 3/4 pages of the book. But, since there's no other book about NURBS, as complete as this, you may want to buy this one or else you can take a look "Mathematical Element for Computer Graphics". It also contains 300 pages of NURBS.
Excellent introduction to splines for the non-mathematician.......2000-02-12
One of the greates assets of this book is that it is fairly comprehensive while still using a minimum amount of mathematics. The style is lucid, easy to follow; the numerous C-like algorithms can be adapted to one's own use, and deal with the most important aspect of NURBS. This is easily the best introductory NURBS text. The only problem I see is the lack of discussion for ray-surface intersection tests, which are necessary if NURBS are to be rendered by raytracing. I recommend "The Nurbs Book" to any engineers and graphics professionals interested in curved surfaces.
Start Point.......1999-12-29
Before owning this book i cassified NURBS as kind of mathematical definitions of curves and surfaces. I was wrong, now it opened my mind so i develop new NURBS surfaces based on well described primitives. Twisting, blending, extruding is good starting point to develop surface definitions you exactly need. How about lofting shapes along branch like path curves?
Book Description
This is the first book to fully address the study of approximation algorithms as a tool for coping with intractable problems. With chapters contributed by leading researchers in the field, this book introduces unifying techniques in the analysis of approximation algorithms.
Customer Reviews:
A good survey on approximation algorithms.......2000-05-09
Developing approximation algorithms for NP hard problems is now a very active field in Mathematical Programming and Theoretical Computer Science. This book is actually a collection of survey articles written by some of the foremost experts in this field.
Many of these developments are due to Mathemtical programming (primal dual, semidefinite programming et al). The most exciting of these has been the Goemans and Williamson algorithm for MAX CUT and MAX SAT. A good account of these techniques appears in Chapters 4 and 11.
On the other hand a sequence of unexpected results in complexity culminated in a proof that many of these problems cannot have polynomial approximation algorithms unless P=NP. A good survey of "Hardness of Approximations" appears in Chapter 10, written by Sanjeev Arora and Carsten Lund both of whom were responsible for some original developments in this field.
I am going to purchase a copy of this book and can only strongly recommend it to everyone.
Average customer rating:
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Bezier and B-Spline Techniques
Hartmut Prautzsch ,
Wolfgang Boehm , and
Marco Paluszny
Manufacturer: Springer
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ASIN: 3540437614 |
Book Description
This book provides a solid and uniform derivation of the various properties Bézier and B-spline representations have, and shows the beauty of the underlying rich mathematical structure. The book focuses on the core concepts of Computer Aided Geometric Design with the intension to give a clear and illustrative presentation of the basic principles, as well as a treatment of advanced material including multivariate splines, some subdivision techniques and constructions of free form surfaces with arbitrary smoothness.
The text is beautifully illustrated with many excellent figures to emphasize the geometric constructive approach of this book.
Customer Reviews:
Good reference maybe.......2006-08-09
I'm not sure what sort of person would find this book useful. If you want to LEARN about Bezier or B-Spline curves, then I don't think this book is for you. The authors' stated goal was to "provide a solid and uniform derivation" of Bezier and B-Spline properties. I believe that they have succeeded, almost every factoid I've seen in other books is included and proved rigorously. What is NOT included is any sort of meaningful explanation of the concepts. The material is presented at a breakneck pace, with everything presented exactly once, and most often in mathematical notation rather than in English. This is a good way to pack a lot of material into a few pages, but it makes for pretty difficult reading. I really don't see how a person could possibly follow the exposition in this book unless they basically already knew the material.
If you already are familiar with Bezier and B-Spline techniques, or perhaps you are an expert in a related field like approximation theory, then you might find this useful.
So if the Authors acheived their stated goal, then why only the 3-star rating? I've recently bought quite a few of these books on splines, in preperation to write a chapter in my own (introductory) 3d math book. Most of the material in this book can be found in other books. Of course, all of the books have significant overlap, since they are covering the same subject. But if you could have a book that covers most of the same material AND also has more exposition, I'd go for the one with the more exposition. I don't think there's enough unique material in this book to trade off the loss of the much more graceful exposition in the other books.
In particular, if you're interested in *learning* about Bezier curves or B-Splines, I found these two books much more accessible:
An Introduction to Splines for use Computer Graphics and Geometric Modeling by Bartels et al. has a much slower pace - paradoxially this means that if you're learning the material, you will be able to read it FASTER since you can maintain a constant pace. It focuses on B-Splines and only stops breifly to mention Bezier curves as a general case.
The other book is Curves and Surfaces for COmputer Aided Geometric Design by Farin. He introduces Bezier curves and fully develops them, at a reasonable pace, before discussing B-splines. I personally found this approach to be better from a teaching perspective, since B-Splines are more abstract and Bezier curves are easier to understand. (Be warned that I have a rather old editition, the 2nd, I believe he's on the 5th now. I don't know what all has changed since then.)
Book Description
- Unique in its survey of the range of topics.
- Contains a strong, interdisciplinary format that will appeal to both students and researchers.
- Features exercises and web links to software and data sets.
Download Description
- Unique in its survey of the range of topics.
- Contains a strong, interdisciplinary format that will appeal to both students and researchers.
- Features exercises and web links to software and data sets.
Customer Reviews:
Great book!!!.......2004-12-07
A must have for anyone interested in otimization! Extremely well written and objective.
Recommended to scholars and graduate students.......2003-09-23
Introduction to Stochastic Search and Optimization provides comprehensive, current information on methods for real-world problem solving, including stochastic gradient and non-gradient techniques, as well as relatively recent innovations such as simulated annealing, genetic algorithms, and MCMC. It is written to be read and understood by graduate students, industrial practitioners, and experienced researchers in the field. Web links to software and data sets, and an extensive list of references of the book allows the reader to explore deeper into certain topic areas. I also found the index to be very comprehensive and carefully done. The appendices are as a refresher and summary of much of the prerequisite material. The book is somewhat unique in providing a balanced discussion of algorithms, including both their strengths and weaknesses. The book is among very few books that have integrated essential parts of statistical fields with optimization and decision making. The book's inclusion of a chapter on optimal experimental design is an example of such integration. The approaches discussed in the book could be used for financial decision making, forecasting, and quality improvement, among many other areas.
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Diophantine Approximation on Linear Algebraic Groups: Transcendence Properties of the Exponential Function in Several Variables
Michel Waldschmidt
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ASIN: 3540667857 |
Book Description
The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function ez: a central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. It includes proofs of the main basic results (theorems of Hermite-Lindemann, Gelfond-Schneider, 6 exponentials theorem), an introduction to height functions and Lehmer's problem, several proofs of Baker's theorem as well as explicit measures of linear independence of logarithms. An original feature is the systematic use, in proofs, of Laurent's interpolation determinants. The most general result is the so-called Theorem of the Linear Subgroup, an effective version of which is also included. It yields new results of simultaneous approximation and of algebraic independence. Two chapters written by D. Roy provide complete and at the same time simplified proofs of zero estimates (due to Philippon) on linear algebraic groups.
Book Description
Since the publication of "Spectral Methods in Fluid Dynamics", spectral methods, particularly in their multidomain version, have become firmly established as a mainstream tool for scientific and engineering computation. While retaining the tight integration between the theoretical and practical aspects of spectral methods that was the hallmark of the earlier book, Canuto et al. now incorporate the many improvements in the algorithms and the theory of spectral methods that have been made since 1988. The initial treatment Fundamentals in Single Domains discusses the fundamentals of the approximation of solutions to ordinary and partial differential equations on single domains by expansions in smooth, global basis functions. The first half of the book provides the algorithmic details of orthogonal expansions, transform methods, spectral discretization of differential equations plus their boundary conditions, and solution of the discretized equations by direct and iterative methods. The second half furnishes a comprehensive discussion of the mathematical theory of spectral methods on single domains, including approximation theory, stability and convergence, and illustrative applications of the theory to model boundary-value problems. Both the algorithmic and theoretical discussions cover spectral methods on tensor-product domains, triangles and tetrahedra. All chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is greatly expanded as are the set of numerical examples that illustrate the key properties of the various types of spectral approximations and the solution algorithms.
A companion book "Evolution to Complex Geometries and Applications to Fluid Dynamics" contains an extensive survey of the essential algorithmic and theoretical aspects of spectral methods for complex geometries and provides detailed discussions of spectral algorithms for fluid dynamics in simple and complex geometries.
Average customer rating:
- This book is very important to my study in guraduate school.
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Asymptotic Approximation of Integrals (Classics in Applied Mathematics)
R. Wong
Manufacturer: SIAM: Society for Industrial and Applied Mathematics
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ASIN: 0898714974 |
Book Description
Asymptotic methods are frequently used in many branches of both pure and applied mathematics, and this classic text remains the most up-to-date book dealing with one important aspect of this area, namely, asymptotic approximations of integrals. In this book, all results are proved rigorously, and many of the approximation formulas are accompanied by error bounds. A thorough discussion on multidimensional integrals is given, with references provided. Asymptotic Approximations of Integrals contains the ‘distributional method’, not available elsewhere. Most of the examples in this text come from concrete applications. Since its publication twelve years ago, significant developments have occurred in the general theory of asymptotic expansions, including smoothing of the Stokes phenomenon, uniform exponentially improved asymptotic expansions, and hyperasymptotics. These new concepts belong to the area now known as ‘exponential asymptotics’. Expositions of these new theories are available in papers published in various journals, but not yet in book form.
Customer Reviews:
This book is very important to my study in guraduate school........1999-03-04
I am studying "Asyptotic Expantions" in graduate school. To study this field, this book is very important reference one of them.
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Algorithms for Minimization Without Derivatives
Richard P. Brent
Manufacturer: Dover Publications
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ASIN: 0486419983 |
Book Description
Outstanding text for graduate students and research workers proposes improvements to existing algorithms, extends their related mathematical theories, and offers details on new algorithms for approximating local and global minima. Many numerical examples, along with complete analysis of rate of convergence for most of the algorithms and error bounds that allow for the effect of rounding errors.
Book Description
This book is based on the author's experience with calculations involving polynomial splines. It presents those parts of the theory which are especially useful in calculations and stresses the representation of splines as linear combinations of B-splines. After two chapters summarizing polynomial approximation, a rigorous discussion of elementary spline theory is given involving linear, cubic and parabolic splines. The computational handling of piecewise polynomial functions (of one variable) of arbitrary order is the subject of chapters VII and VIII, while chapters IX, X, and XI are devoted to B-splines. The distances from splines with fixed and with variable knots is discussed in chapter XII. The remaining five chapters concern specific approximation methods, interpolation, smoothing and least-squares approximation, the solution of an ordinary differential equation by collocation, curve fitting, and surface fitting. The present text version differs from the original in several respects. The book is now typeset (in plain TeX), the Fortran programs now make use of Fortran 77 features. The figures have been redrawn with the aid of Matlab, various errors have been corrected, and many more formal statements have been provided with proofs. Further, all formal statements and equations have been numbered by the same numbering system, to make it easier to find any particular item. A major change has occured in Chapters IX-XI where the B-spline theory is now developed directly from the recurrence relations without recourse to divided differences. This has brought in knot insertion as a powerful tool for providing simple proofs concerning the shape-preserving properties of the B-spline series.
Customer Reviews:
Good book, I like it.......2007-03-09
The book I bought arrived just as I expected, in one week. It's in excellent condition, no markings inside, clean and neat. Thanks a lot.
de Boor's "A Practical Guide to Splines".......2005-06-14
This is absolutely the most excellent book on the subject ever written. It is rigorous, accessible to those who are not professional mathematicians, and full of examples. Using de Boor's public domain software is a cinch, but you need to read the book to fully understand how to do it properly. I really wonder how I got along without it all these years.
Splines are more than you thought.......2000-05-09
This is a very nice book about splines for all who needs interpolation of data and are getting a bit nervous about the somewhat improper behaviour of normal cubic splines, i.e., the ones you learned about in your undergrad exam. The author provides both illustrative examles with computer codes (in FORTRAN) and describes the necessary theoretical background. Compared with many other books, it is readable also for a non-mathematician, although some experience with numerical analysis will be most helpful.
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