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Theory of Approximation 4 reviews
N. I. Achieser
Dover Publications, 1992
The fundamentals.
Even at a time when a subject undergoes a revolution, and new directions keep coming, new methods; even brand new and different applications--- even then are there central ideas that are constant, the fundamentals. Within mathematics, approximation theory is such a field: In the past decade, we have seen a host of such new developments: wavelet approximations, fast computational algorithms with ...
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Quantum Theory of the Electron Liquid5 reviews
Gabriele Giuliani, Giovanni Vignale
Cambridge University Press, 2005
An outstanding job
Written with the student in mind, this book gives an excellent introduction to density functional theory, many-body quantum theory, and their application to the physical system now known as the electron liquid. Given the current interest in electron liquids, both from an applied and a theoretical standpoint, this book serves a need for those who want to educate themselves on the different ...
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Approximation Algorithms6 reviews
Springer, 2004
Very nice introduction
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. ...
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Introduction To Engineering Design and Problem Solving2 reviews
Arvid R. Eide, Roland Jenison, ...
McGraw-Hill Science/Engineering/Math, 2001
Solid Foundation for Engineers and Designers
I actually ended up reading this book after getting my master's degree in aerospace engineering, and even after a few years of work in industry. This was because my first crack at doing real aircraft structural design work put me completely in over my head, and this book was the first step of getting a handle on everything. In retrospect I'm completely aghast that in six years and two degrees of ...
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Wavelets through a Looking Glass (Applied and Numerical Harmonic Analysis)7 reviews
Ola Bratteli, Palle Jorgensen
Birkhäuser Boston, 2002
A fresh look at wavelets
The Book by Bratteli and Jorgensen is a superb book on wavelet's theory. It is very well written and has new and a fresh point of view on the subject. Although there are several good books on wavelets, the book by Bratteli and Jorgensen covers an important niche that has not been covered before. In particular 1- The book covers the theory of wavelets from the point of view of operators and ...
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Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties3 reviews
G. Ausiello, P. Crescenzi, ...
Springer, 2003
A great sequel to Garey and Johnson
This book is a great sequel to Garey and Johnson. The appendix of this book gives a list of all NP optimisation problems together with their current approximability (or inapproximability results) in a Garey Johnson fashion. Developing approximation algorithms for NP hard problems is now a very active field in Mathematical Programming and Theoretical Computer Science. There have been a number of ...
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Introduction to Stochastic Search and Optimization2 reviews
James C. Spall
Wiley-Interscience, 2003
Recommended to scholars and graduate students
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 ...
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Quantum Mechanics from General Relativity: An Approximation for a Theory of Inertia (Fundamental Theories of ...3 reviews
M. Sachs
Springer, 1986
A brilliant sequel to GRM
Starting with a detailed comparison of the original intentions of Bohr and Einstein in their development of Quantum Mechanics and General Relativity, Sachs shows that the goals of General Relativity are more insightful and subsume those of Quantum Mechanics. Where General Relativity is the forest, Quantum Mechanics is the trees. By introducing the spinor variables of General Relativity that Sachs ...
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Asymptotic Methods in Analysis4 reviews
N. G. de Bruijn
Dover Publications, 1981
A Classic
This is a Classic introduction to Asymptotics. Its main strength, is the illustration of techniques through the detailed working out of examples. In addition, there is FULL rigour, so that the proofs are complete. To study this book you should be comfortable with: a) Undergraduate Level Real Analysis. b) Elementary Notions from Complex Variable Theory including Complex Integration, Calculus of ...
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Meshfree Approximation Methods with MATLAB (Interdisciplinary Mathematical Sciences) (Interdisciplinary ...3 reviews
Gregory F. Fasshauer
World Scientific Publishing Company, 2007
Solid Book
This book is an excellent text. The use of radial basis functions for approximation and collocation is widespread, but there are few texts which provide both the theoretical foundation and application of their use. Greg Fasshauer has produced an extremely useful guide for both novices and experts and it will certainly be around for some time.
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Approximating Integrals Via Monte Carlo and Deterministic Methods1 review
Michael Evans, Tim Swartz
Oxford University Press, USA, 2000
Everything in one place
This book has lots of information about estimating integrals all in one place. The text is very readable and has clearly explained examples throughout. I would recommend this book to anyone who does work using computers to calculate integrals.
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Numerical Solution of Stochastic Differential Equations (Stochastic Modelling and Applied Probability)2 reviews
Peter E. Kloeden, Eckhard Platen
Springer, 2000
Excellent
This book is one of the finest written on the subject and is suitable for readers in a wide variety of fields, including mathematical finance, random dynamical systems, constructive quantum field theory, and mathematical biology. It is certainly well-suited for classroom use, and it includes computer exercises what are definitely helpful for those who need to develop actual computer code to solve ...
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Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and ...1 review
Athanasios C. Antoulas
Society for Industrial and Applied Mathematic, 2005
An Excellent Book on Model Order Reduction
Dr. Athanasios C. Antoulas is one of the world's leading authorities on model order reduction. In this book he clearly differentiated Singular Value Decomposition (SVD) methods and Krylov subspace projection methods and their explanation in part III and IV is excellent. The fist two chapter of introduction and preliminaries give you sufficient background to understand Part III and IV. The book ...
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Approximately Calculus1 review
Shahriar Shahriari
American Mathematical Society, 2006
Good book with many hard problems
Explores Calculus in a novel way. Has many good calculus questions and some elementary number theory problems as well. Only drawback is that its impossible to find the solutions to the problems in the book.
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Smoothing Spline ANOVA Models2 reviews
Chong Gu
Springer, 2002
smoothing splines extended to mutivariate data
The smoothing approach to density estimation and regression began with kernel methods in the 1950s and 1960s. For regression problems, smoothing splines were introduced using roughness penalties in the early pioneering work of Kimeldorf and Wahba 1970 & 1971 and the famous paper by Good and Gaskins in 1971. Since that time some excellent books have been written for univariate analysis based on ...
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Approximation Methods for Electronic Filter Design1 review
Richard W. Daniels
McGraw-Hill Inc.,US, 1974
Deriving Filter Transfer Functions
As the title implies, this book focuses on the Approximation problem, that is formulating the best realizable transfer function for a given filter application. Advanced mathematical topics such as elliptic functions, with which engineers aren't routinely familiar, are covered in detail before they are used to find transfer functions. The book touches on the Synthesis problem, in which the actual ...
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Approximation Algorithms for NP-Hard Problems1 review
Course Technology, 1996
A good survey on approximation algorithms
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 ...
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Approximation Theorems of Mathematical Statistics1 review
Robert J. Serfling
Wiley-Interscience, 2001
Great Reference
As a graduate student in statistics, I have had plenty of opportunities to browse through the pages of this book in search of that theorem, technique, or tool that would be applicable to my own work. In many occasions I was succesful in such search. This title compiles and synthesizes a wealth of definitions, theorems, and techniques classically used in asymptotic theory of estimators. It is ...
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Approximation Theory: From Taylor Polynomials to Wavelets (Applied and Numerical Harmonic Analysis)1 review
Ole Christensen, Khadija L. Christensen
Birkhäuser Boston, 2005
Outstanding book and a fast read
The book is very well written. Very clear and makes for a fast read. Only drawback is all notation is not completely defined; however, this problem has only been observed in very few instances. Overall, very well done!
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Optimization: Algorithms and Consistent Approximations (Applied Mathematical Sciences)2 reviews
Elijah Polak
Springer, 1997
superbly written ... work of art.
Develops a powerful algorithmic and implementable framework for solving finite and semi-infinite nonlinear optimization problems with a special emphasis on min-max optimization problems.
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