Average customer rating:
- very nice conceptual overview
- Not for the practitioner
- Trash
- Excellent Introduction, Sparse on Details
- A Good Introductory Survey
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Scientific Computing
Michael T. Heath
Manufacturer: The McGraw-Hill Companies, Inc.
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ASIN: 0072399104 |
Book Description
Heath 2/e, presents a broad overview of numerical methods for solving all the major problems in scientific computing, including linear and nonlinear equations, least squares, eigenvalues, optimization, interpolation, integration, ordinary and partial differential equations, fast Fourier transforms, and random number generators. The treatment is comprehensive yet concise, software-oriented yet compatible with a variety of software packages and programming languages. The book features more than 160 examples, 500 review questions, 240 exercises, and 200 computer problems. Changes for the second edition include: expanded motivational discussions and examples; formal statements of all major algorithms; expanded discussions of existence, uniqueness, and conditioning for each type of problem so that students can recognize "good" and "bad" problem formulations and understand the corresponding quality of results produced; and expanded coverage of several topics, particularly eigenvalues and constrained optimization. The book contains a wealth of material and can be used in a variety of one- or two-term courses in computer science, mathematics, or engineering. Its comprehensiveness and modern perspective, as well as the software pointers provided, also make it a highly useful reference for practicing professionals who need to solve computational problems.
Customer Reviews:
very nice conceptual overview.......2006-07-22
Wow, people seem to be really split on this book. I had Mike Heath for numerical analysis/scientific computing and he was an excellent instructor, one of the best lecturers I've ever had. (As a consequence, I have a hard time separating the book and the class, so judge accordingly.) The book is based on his lecture notes, though he added some material and didn't cover every topic in the book. Just reading the book is useful to give you an overview of the point behind different methods. The goal of the class for which this book was written is actually quite conceptual. It was to give scientists (that's me: a stats researcher who makes heavy use of numerical computation) and CS people in areas other than scientific computing a leg up. It was only a first class for people in scientific computing, the rough equivalent of intro Physics or intro Probability/Stats for people in those respective majors. However, you *won't* be prepared to "roll your own" from this book. In fact, at the beginning of the semester Heath was very careful to note that if you have the opportunity to use a library function for most numerical programming, you are nuts to roll your own. Why? Numerical algorithms are usually extremely complicated and the authors of the code often spend years developing careful expertise on them. Frequently the formulas used to elucidate a given method are NOT the ones used to implement it. You need error traps, tricks to handle ill-scaling and other special cases, etc. These are things that someone who has a one-semester, superficial understanding of a topic simply won't have. So consider the book on the goals it set: it is an overview of a field. If you want to learn more about any one topic, you have to dig deeper and consult references and other works, but this is a good place to start. For this, the book serves admirably.
Not for the practitioner.......2005-11-17
If you are interested in Scientific computing from the viewpoint of the end user that is the guy who uses the method to solve practical engineering problems then this book is lacking.
Not enough methods in this book to constitute an introductory survey of the field. Every chapter gets heavy dose mathematical treatment, apparently Heath loves his math but for the rest of us it doesnt translate into know-how. Know how to solve equations using computational techniques. Very few derivations to back his mathematical swagger, very few examples (if any) and fewer numerical schemes to solve problems. Many of the chapters receive cursory treatment such as PDE's get about 70 pages of print. Far too little to do anyone any good.
He does talk about interesting issues such as conditioning and error analysis and computer precision and memory issues but it is done from such a superficial viewpoint that one cannot use anything to improve ones code. Not recommended if you want to learn numerical methods even if you have an excellent professor to learn from. His chapter on FFT's was even more abstruse and there was hardly any methods with which to solve PDE's.
I had this for a graduate course in Numerical Methods but ended up using Hoffman's excellent book on Numerical Methods.
Trash.......2005-10-14
If you want to have a solid understanding of numerical computation, this book is definitely the last choice. Many theorems are given without any proof or even intuitions behind them in this book. Even when a proof is provided, it's often far from rigorous. The organization of chapters is the worst I have ever seen, revelant materials are scattered over several different locations rather than put together. Take the SVD for example, it is mentioned in the end of chapter 3, but reappears in chapter 4, which is very confusing. If you are new to this area, please don't read this book. It gives you many many facts without explanations, which I think is not a good way to learn new things. David S. Watkins' Fundamentals of Matrix Computations is a lot better and easier to understand. It also emcompasses many detailed treatments of various theorems. If you have bought Heath's book, don't be sad, at least it can serve as a coaster.
Excellent Introduction, Sparse on Details.......2004-11-20
While sparse on the details of many of the algorithms and theorems mentioned, as an introduction it covers a broad range of material-enough for two semesters of study. The writing is lucid, and when a proof of a theorem is given, it is easy to follow and explained in english afterward. Rationale is given for everything, which is a great benefit to a student not familiar with the nuances of sophisticated linear algebra.
A Good Introductory Survey.......2002-11-05
This book excels at presenting a reader with little to no knowledge in computer science and a mild mathematical background (knowledge of differential equations as a prerequisite) with the fundamental concepts regarding scientific computing. The presentation of pseudo-code algorithms helps smooth the transition from analytical (pencil and paper) thinking to numerical thinking. The algorithms are presented in a manner such tha anyone with access to dozens of possible environments can apply them, though they are by no means complete, thus requiring some thought into the processes. The material covered is 110% of what an engineer will want to know, 90% of what an applied mathematician will want to know, and 45% of what a numerical analyist will want to know. In all, a great book to begin a foray into numerical computing.
Book Description
Available for the first time in paperback, R. Tyrrell Rockafellar's classic study presents readers with a coherent branch of nonlinear mathematical analysis that is especially suited to the study of optimization problems. Rockafellar's theory differs from classical analysis in that differentiability assumptions are replaced by convexity assumptions. The topics treated in this volume include: systems of inequalities, the minimum or maximum of a convex function over a convex set, Lagrange multipliers, minimax theorems and duality, as well as basic results about the structure of convex sets and the continuity and differentiability of convex functions and saddle- functions.
This book has firmly established a new and vital area not only for pure mathematics but also for applications to economics and engineering. A sound knowledge of linear algebra and introductory real analysis should provide readers with sufficient background for this book. There is also a guide for the reader who may be using the book as an introduction, indicating which parts are essential and which may be skipped on a first reading.
Customer Reviews:
Very Good.......2007-05-09
This book is a classic. It is probably the best reference book although it is tough to read from the beginning untill the end. The style is heavy and you need strong mathematical background to understand it.
Anyway, if you need a result on convex functions or convex analysis it is very likely that you will find it in ths book.
the only thing it lacks is diagrams.......2007-01-12
This book perhaps ranks with Halmos' "Finite Dimensional Vector Spaces" as an unusually clear description of its subject. Rockafellar's book has been through numerous printings in 40 years. The theorem proofs can be intricate. But the thread of logical development makes reading it worthwhile. Certainly, it is beautiful how the crucial assumption of convexity makes all the derivations possible.
The level of discussion is suitable for a 3rd year undergrad [or higher], who is majoring in maths.
By current standards of maths texts, it does lack diagrams. In fact, there doesn't seem to be a single one! Something to get used to, if you are a current undergrad weaned on recent texts. [Since the author is still alive, perhaps he might consider adding diagrams to a future edition.]
a beauty mummified .......2005-12-02
convex programming is a beautiful topic which admits amazing geometric interpretation.
books like this manage to destroy one's appreciation of the topic by not providing even one (gasp!) figure. damn Bourbaki style.
Excellent introduction to Topology........2001-05-10
This is a good book for the first year in PhD studies. I recommend amply this book, it's very clear in the explanation, if you have any doubts about topology, Rockafellar explained in this book very simple the theory and all you need about Topology.
Book Description
A bottom-up approach that enables readers to master and apply the latest techniques in state estimation
This book offers the best mathematical approaches to estimating the state of a general system. The author presents state estimation theory clearly and rigorously, providing the right amount of advanced material, recent research results, and references to enable the reader to apply state estimation techniques confidently across a variety of fields in science and engineering.
While there are other textbooks that treat state estimation, this one offers special features and a unique perspective and pedagogical approach that speed learning:
* Straightforward, bottom-up approach begins with basic concepts and then builds step by step to more advanced topics for a clear understanding of state estimation
* Simple examples and problems that require only paper and pen to solve lead to an intuitive understanding of how theory works in practice
* MATLAB(r)-based source code that corresponds to examples in the book, available on the author's Web site, enables readers to recreate results and experiment with other simulation setups and parameters
Armed with a solid foundation in the basics, readers are presented with a careful treatment of advanced topics, including unscented filtering, high order nonlinear filtering, particle filtering, constrained state estimation, reduced order filtering, robust Kalman filtering, and mixed Kalman/H? filtering.
Problems at the end of each chapter include both written exercises and computer exercises. Written exercises focus on improving the reader's understanding of theory and key concepts, whereas computer exercises help readers apply theory to problems similar to ones they are likely to encounter in industry. A solutions manual is available for instructors.
With its expert blend of theory and practice, coupled with its presentation of recent research results, Optimal State Estimation is strongly recommended for undergraduate and graduate-level courses in optimal control and state estimation theory. It also serves as a reference for engineers and science professionals across a wide array of industries.
A solutions manual is available upon request from the Wiley editorial board.
Customer Reviews:
The best book on Kalman filters.......2007-08-13
I have 4 books on Optimal state estimation:
_ Applied Optimal Estimation of Arthur Gelb.
_ Optimal Control and Estimation by Robert F. Stengel
_ Optimal Control and Estimation Theory by George M. Siouris
_ Optimal State Estimation By Dan Simon
Of the 4, Dan Simon's Optimal State Estimation is by far the most useful for a GNC Engineer like me. He strikes a good balance between theory and practice and his examples are really useful. I find his treatment of EKF excellent.
Excellent treatment of nonlinear filtering, especially filters related to unscented transforms.......2007-07-25
I'm using this book to apply the unscented Kalman filter to multiple sensor target tracking. His exposition on the unscented transforms is very clear.
I read some articles of Prof. Dan Simon in Embedded.com.......2006-12-10
I found his articles are intuitive and useful for my research.
If you are engineer who need to apply observer and estimation into your work. This book is good book.
Average customer rating:
- worst ever!!!
- How to learn and use MATLAB quickly!
- Great self teaching tool
|
Applied Optimization with MATLAB Programming
P. Venkataraman
Manufacturer: Wiley-Interscience
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ASIN: 0471349585 |
Book Description
A new approach to learning classical optimization methods-numerical techniques modeled and illustrated via MATLAB
This unique and timely volume combines a formal presentation of classical methods of design optimization with detailed instruction in the application of these methods using MATLAB. It introduces readers to the symbolic, numerical, and graphic features of MATLAB and integrates this powerful combination in the translation of many algorithms into applied optimization techniques with animation.
Applied Optimization with MATLAB® Programming develops all necessary mathematical concepts, illustrates abstract mathematical ideas of optimization using MATLAB's rich graphics features, and introduces new programming skills incrementally as optimization concepts are presented. This valuable learning tool:
- Focuses on real-world optimization techniques
- Covers all areas of optimization, including linear, nonlinear, discrete, and global
- Includes creative examples from many disciplines
- Presents a number of practical, open-ended design problems
- Features an accompanying Web site with MATLAB code for all the numerical techniques and examples in the book
This one-of-a-kind resource enables senior-undergraduate and graduate students in engineering and other design disciplines to develop practical programming skills as they master the concepts of optimization. It is also an excellent self-teaching guide for design engineers in all fields of endeavor.
Customer Reviews:
worst ever!!!.......2004-01-29
I've had Dr. Venkat as a professor for 3 classes at RIT and he is by far the worst I have ever had. DO NOT BUY HIS BOOK! It will only make you dumber! That is how I feel after coming out of his class. I believe the reviewer that says the website is a main resource, he points us to the class site all the time with no helpful information, and because he can't answer the questions himself on the spot. Are you buying a book or a website? I think that's all the helpful information I have for now.
How to learn and use MATLAB quickly!.......2002-11-03
Excellent source for all people who don't have time to study MATLAB in-depth. A lot of useful examples help anyone to create his/her own code in no time!
Great self teaching tool.......2002-01-03
In this text the author chooses MATLAB as the tool in running computer-based optimization problems. This approach clearly covers all levels of optimization, and the book further supports this coverage through many helpful examples that balance theory with the application. The open-ended problems that are provided are a helpful mechanism for reinforcing the lessons of the text. The website that is a companion to the book, helped me access the reference links to the MATLAB software and the author's own personal site. This web site is a true lifeline to the book.
Average customer rating:
- not enough
- Doubles as inexpensive textbook on operations research
- Schaum's Outline of Operations Research
- Solved problems book
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Schaum's Outline of Operations Research
Richard Bronson , and
Govindasami Naadimuthu
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ASIN: 0070080208 |
Book Description
Tackling the broad range of allocation problems that actually confront engineers, programmers and analysts in today's business and industrial worlds, this book takes readers step-by-step through all the mathematical programming techniques--including the trailblazing Karmarkar algorithm--needed to excel in any operations research course. It's easy to see why the first edition of this invaluable study guide sole more than 35,000 copies! It cuts down study time while it builds essential skills.
Customer Reviews:
not enough.......2007-01-23
First of all, be careful, this is not a text book. It has a good presentation for problem solution. First, there are a some solved problems, then supplementary problems are coming. The answers of supplementary problems are at the end of the book.
This book might be useful for beginners. For every topic, there are easy problems, not specific problems similar to case studies. If you are over beginner degree, this book will not be useful for you. Especially, integer programming sections are not satisfactory. For instance, there isn't any facility location problem solution.
To sum-up this book may be useful for a beginner as a workbook.
Doubles as inexpensive textbook on operations research.......2006-04-15
Some of the primary tools used by operations researchers are statistics, optimization, stochastics, queueing theory, game theory, graph theory, and simulation. Because of the computational nature of these fields operations research also has ties to computer science, and thus this outline is useful to people from both fields. OR is concerned with optimization problems in which one seeks to maximize or minimize a specific quantity. The first part of this book is on optimization via linear, integer, and nonlinear programming. Next, network analysis is covered. Network analysis is the general name given to certain specific techniques which can be used for the planning, management and control of projects. Two different techniques for network analysis were developed independently in the late 1950's - PERT (Program Evaluation and Review Technique) and CPM (Critical Path Management). These techniques are also covered in the outline. The next subject tackled is that of inventory models - allowing shortages, allowing price discounts, risk conditions, etc., and their mathematical modeling. Game theory, decision theory, and dynamic programming are all explained in the context of inventory models and forecasting. Finally, there is coverage of Markov chains and queueing theory. Queuing Theory arises from the use of mathematical analysis to theoretically describe production processes along with statistical/probabilistic techniques to account for varying dynamic patterns within the stages of a productive process. The problem to be met is simply entitled "congestion", what happens when a system does not operate smoothly or efficiently.
I really liked this Schaum's outline, and I used it to teach myself most of the mathematical processes covered without the need for any additional resources. The theory is given in small doses along with very illustrative examples. The mathematics starts with simple algebra and works up to nothing more complex than probability and statistics. I highly recommend it for anybody enrolled in an operations research class as well as computer scientists and mathematics students that are studying any subset of the topics covered in this book.
Schaum's Outline of Operations Research.......2002-07-21
i found this book to be a very helpfull tool a long with my text book.it excels in its simplicity and a wide varity of examples and solved problems written in plain english.
hope you like it too.
thank you.
M. Madain.
Solved problems book.......2001-06-13
Originally the book of Richard Bronson(1982) was very useful for the solution of simple problems, then a difficult one, but it is always required a text book accompany this. The students of my classes need all the time solved problems to practice.
Average customer rating:
|
A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems (Nonconvex Optimization and Its Applications)
Hanif D. Sherali , and
W.P. Adams
Manufacturer: Springer
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ASIN: 0792354877 |
Book Description
This book addresses a new method for generating tight linear or convex programming relaxations for discrete and continuous nonconvex programming problems. Problems of this type arise in many economics, location-allocation, scheduling and routing, and process control and engineering design applications. The principal thrust is to commence with a model that affords a useful representation and structure, and then to further strengthen this representation through an automatic reformulation and constraint generation technique. The contents of this book comprise the original work of the authors compiled from several journal publications, and not covered in any other book on this subject. The outstanding feature of this book is that it offers for the first time a unified treatment of discrete and continuous nonconvex programming problems. In essence, the bridge between these two types of nonconvexities is made via a polynomial representation of discrete constraints. The book lays the foundation of an idea that is stimulating and that has served to enhance the solubility of many challenging problems in the field.
Audience: This book is intended for researchers and practitioners who work in the area of discrete or continuous nonlinear, nonconvex optimization problems, as well as for students who are interested in learning about techniques for solving such problems.
Book Description
There has been a great deal of excitement over the last few years concerning the emergence of new mathematical techniques for the analysis and control of nonlinear systems: witness the emergence of a set of simplified tools for the analysis of bifurcations, chaos and other simplified tools for the analysis of bifurcations, chaos and other complicated dynamical behaviour and the development of a comprehensive theory of nonlinear control. Coupled with this set of analytic advances has been the vast increase in computational power available both for the simulation of nonlinear systems as well as for the implementation in real time of sophisticated, real-time nonlinear control laws. Thus, technological advances have bolstered the impact of analytic advances and produced a tremendous variety of new problems and applications which are nonlinear in an essential way. This book lays out in a concise mathematical framework the tools and methods of analysis which underlie this diversity of applications. The material presented in this book is culled from different 1st year graduate courses that the author has taught at MIT and at Berkeley.
Customer Reviews:
Good book........2007-08-03
This is a good book devoted to nonlinear systems.
Compared to Vidyasagar's book, this book has more mathematical rigour, therefore, to follow it you should have a good Calculus/Linear Algebra /
Analysis background (I recomend to have good books of these subjects while reading Sastry).
Some topics are more intuitively than explictly covered. The same thing occurs in the exercises at the end of the chapters. Because of this I think that you should not follow only this book in a first course on nonlinear systems. I recomend Khalil's and Isidori's book as parallel readings.
An excellent nonlinear systems book.......2001-04-14
As a Ph.D student I found this book very helpful and I would like to recommend this book everyone involved in nonlinear systems. I also have Vidyasagar's (i wish there were more example problems) and Khalil's nonlinear systems(mainly devoted to Lyapunov analysis) books which are also good but I found this book much explanatory than others.
Book Description
This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or ‘quasi-Newton’ methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems.
Customer Reviews:
SIAM calls this book a "Classic" for good reason. .......2006-09-25
The ultimate self-teaching book for Newton-type algorithms that address small or large systems of nonlinear equations. A comprehensive treatment of general unconstrained optimization, least-squares optimization, and also well-determined systems. Unusually well-written, with a nice blend between underlying theory and practical implementation requirements. Complete pseudo-code within the appendix enables one to create their own program in any language. Alternatively, Fortran source code created by the authors (UNCMIN) can be obtained from Netlib on the web. SIAM calls this book a "Classic" for good reason.
I understood it!.......2000-12-01
Looking for a text that explains the maths and the implementation of optimisation? I needed to write a program that included numerical optimisation, but I didn't understand the maths. I'd tried to read some other books on the subject, but I gave up because they presumed too much background knowledge and because they were written in an academic format (all proofs, greek letters and algebra) too obscure for me to wade through.
This book explains everything in plain english. When there is a new concept to be introduced, they begin with a practical example of the problem and then step through the solution. Any proofs are accompanied by graphs and words. The emphasis is on practicality and concepts rather than algebraic rigour.
I recommend this book to anyone who needs to create their own optimisations, or who wants to understand what goes on inside their software.
Book Description
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures.
The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern topics such as optimality conditions and numerical methods for problems involving nondifferentiable functions, semidefinite programming, metric regularity and stability theory of set-constrained systems, and sensitivity analysis of optimization problems.
Based on a decade's worth of notes the author compiled in successfully teaching the subject, this book will help readers to understand the mathematical foundations of the modern theory and methods of nonlinear optimization and to analyze new problems, develop optimality theory for them, and choose or construct numerical solution methods. It is a must for anyone seriously interested in optimization.
Customer Reviews:
An interesting and useful book.......2007-01-06
The most important feature of this book is the systematic, theory-driven presentation. Proofs of all statements are supported by instructive examples in statistics, finance, economics, and engineering. The analysis covers a broad array of problems, including nondifferentiable and nonconvex. The chapter on duality contains several interesting economic applications. Methods are presented in a transparent way, with convergence proofs and rate of convergence estimates. The chapter on methods for nondifferentiable optimization is quite valuable, because there are few sources with this material. Solutions to problems, some of which are tricky, would help, and I hope that they will be included in the next edition.
Excellent introduction to theory and algorithms for nonlinear optimization.......2006-12-08
This outstanding book fills the need for a recent introductory graduate textbook in nonlinear convex optimization. The book is divided into 2 parts: Part I deals with theory while Part II deals with algorithms for nonlinear convex optimization. Topics covered in Part I include basic convex analysis, optimality conditions, and Lagrangian duality. There are a number of interesting examples distributed throughout the discussions in Part I - some of these examples include recent concepts like semidefinite programming. The author also highlights the importance of DIFFERENTIABILITY in convex optimization - in fact he devotes separate sections for the optimality conditions of smooth convex and nonsmooth convex problems. Part II discusses algorithms for smooth unconstrained and constrained optimization and finally subgradient, bundle, and trust region schemes for nondifferentiable optimization. The discussion on algorithms for nondifferentiable optimization is new and an important ingredient in this book - for more details one can refer to the 2 volume set by Hiriart-Urruty and Lemarechal. However, there is no discussion on INTERIOR POINT METHODS and this is the only notable omission in the book. For more on interior point methods in nonlinear optimization, one can refer to the recent book by Nocedal and Wright. Personally, I enjoyed this book immensely, and I look forward to using it in a graduate course on nonlinear optimization.
Book Description
Problems with multiple objectives and criteria are generally known as multiple criteria optimization or multiple criteria decision-making (MCDM) problems. So far, these types of problems have typically been modelled and solved by means of linear programming. However, many real-life phenomena are of a nonlinear nature, which is why we need tools for nonlinear programming capable of handling several conflicting or incommensurable objectives. In this case, methods of traditional single objective optimization and linear programming are not enough; we need new ways of thinking, new concepts, and new methods - nonlinear multiobjective optimization. Nonlinear Multiobjective Optimization provides an extensive, up-to-date, self-contained and consistent survey, review of the literature and of the state of the art on nonlinear (deterministic) multiobjective optimization, its methods, its theory and its background. The amount of literature on multiobjective optimization is immense. The treatment in this book is based on approximately 1500 publications in English printed mainly after the year 1980. Problems related to real-life applications often contain irregularities and nonsmoothnesses. The treatment of nondifferentiable multiobjective optimization in the literature is rather rare. For this reason, this book contains material about the possibilities, background, theory and methods of nondifferentiable multiobjective optimization as well. This book is intended for both researchers and students in the areas of (applied) mathematics, engineering, economics, operations research and management science; it is meant for both professionals and practitioners in many different fields of application. The intention has been to provide a consistent summary that may help in selecting an appropriate method for the problem to be solved. It is hoped the extensive bibliography will be of value to researchers.
Customer Reviews:
Valuable reference for nonlinear optimisation.......2001-01-06
As a Grad Student , involved in Research work related to Multiobjective NonLinear programming this book has been found to be very useful in its coverage of the theory that one needs to possess to carry on this work.The good thing about it is that it addresses the Discrete world of mathematics also which gives the researcher a broader understanding.It is also nice to have one single book concentrating on various aspects on how to generate Pareto Optima solutions rather than having to go back and read up a number of papers and still be unclear about the subject.All statements are supported with proofs and that makes this a comprehensive and dependable reference.I would like to congratulate the author Dr.Meittinnen for his work and wish him good luck for all other works too.
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