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| | Approximation - Wikipedia, the free encyclopedia |
 | | The type of approximation used depends on the available information, the degree of accuracy required, the sensitivity of the problem to this data, and the savings (usually in time and effort) that can be achieved by approximation. | | | Approximations may be used because incomplete information prevents use of exact representations. | | | An approximation is an inexact representation of something that is still close enough to be useful. |
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http://en.wikipedia.org/wiki/Approximation
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| | Approximation Methods Panel |
| | Approximation methods are becoming popular tools for modeling uncertainty and reducing the computational expense of probabilistic analysis during probabilistic design optimization. | | | Approximation models are employed for f(x), g(x), and S(x,u) to reduce the computational expense of these analyses. | | | He stated that approximation methods are finding new uses in reducing the computational expensive of probabilistic analysis to make probabilistic optimization more tractable. |
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http://www.me.psu.edu/simpson/approximation/approx-panel.html
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| | 550.770 Approximation Algorithms |
| | Trading-off optimality in favor of tractibility is the paradigm of approximation algorithms. | | | Approximation algorithms have developed in response to the impossibility of solving a good many problems exactly. | | | In the case of NP-Complete problems, we sacrifice optimality in favor of a ``good'' solution that can be computed efficiently. |
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http://www.cs.jhu.edu/%7Ecowen/approx.html
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| | The Normal Approximation to the Binomial |
| | Exercise #1 computes binomial probabilities and quantiles for the distribution of girl births and compares them to probabilities computed approximately using a normal approximation. | | | Example #1 computes binomial probabilities and quantiles for the distribution of hotel room occupancies and compares them to probabilities computed approximately using a normal approximation. | | | can be used to experiment with computing approximate and exact binomial probabilities and to assess the conditions for which the normal approximation to the binomial distribution is good. |
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http://www.stat.wvu.edu/SRS/Modules/NormalApprox/normalapprox.html
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| | Approximation Algorithms |
| | Approximation Algorithms for Covering with Fixed Size Hypersquares and Related Problems, Proceedings of the 29th Annual Allerton Conference on Communications, Control and Computing, October 1990, pp. | | | An Efficient Approximate Algorithm for the Kolmogorov--Smirnov and Lilliefors Tests, (with S. Sahni and W. Franta), Journal of Statistical Computation and Simulation, Vol. | | | Complexity and Approximations for Multimessage Multicasting, Journal of Parallel and Distributed Computing, 55, 1998, 215 -- 235. |
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http://www.cs.ucsb.edu/~teo/publications/APROX.html
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| | Eva Tardos, Department of Computer Science, Cornell University |
| | A Constant Factor Approximation Algorithm for a Class of Classification Problems, In the Proceedings of the ACM Symposium on the Theory of Computing, May 2000. | | | My research is concerned with the design and analysis of algorithms for fundamental problems in network, combinatorial optimization, approximation algorithms, on-line algorithms, linear and integer programming, and their applications to various problems. | | | A constant-factor approximation algorithm for the k-median problem. |
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http://www.cs.cornell.edu/People/eva/eva.html
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| | Approximation Algorithms |
| | 236521 is a course on approximation algorithms for NP-hard combinatorial optimization problems given for the second year at the Technion's Computer Science Department. | | | Handout 6: A taxonomy of divide-and-conquer approximation algorithms. | | | Lecture 8: Approximating minimum multicuts; review of semidefinite programming. |
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http://www.cs.technion.ac.il/~rabani/236521.95.wi.html
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| | Approximation algorithm - Education - Information - Educational Resources - Encyclopedia - Music |
| | In computer science, approximation algorithms are an approach to attacking NP-hard optimization problems. | | | Another limitation of the approach is that it applies only to optimization problems and not to “pure” decision problems like Satisfiability. | | | A typical example for an approximation algorithm is the one for vertex cover: Find an uncovered edge and take both end points into the vertex cover. |
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http://www.music.us/education/A/Approximation-algorithm.htm
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| | Approximation Algorithms(Part I of II) |
| | The approximation algorithms approach is particularly suitable for use in the context of integer programming algorithms because the analysis provides a feasible approximate solution as well as a "bound" that leads to an estimate on the gap between the optimal and the feasible solutions. | | | Approximation algorithms have emerged as a major tool for coping with intractability of problems. | | | There are current efforts to unify the ad hoc techniques that have been used for approximation algorithms. |
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http://www.siam.org/meetings/dm98/ms18.htm
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| | David B. Shmoys |
| | The primary focus of my research is on the design and analysis of efficient algorithms for discrete optimization problems, and in particular, on approximation algorithms for NP-hard and other computationally intractable problems. | | | Analogously, from a theoretical perspective, for some NP-hard optimization problems it is possible to efficiently compute solutions that are guaranteed to be arbitrarily close to optimal, whereas for others, computing even a crude approximation to the optimum is also NP-hard. | | | Since the primary means of solving these problems (to optimality) also involves the solution of a sequence of such relaxations, this algorithmic approach dovetails well with the foremost technology for proving optimality, and hence has substantial potential for improving these optimization techniques as well. |
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http://www.orie.cornell.edu/%7Eshmoys
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| | Backprop Learning Tool |
| | In each case, the dotted line is the underlying function to be approximated, the solid line is the neural net output, and the open circles indicate the data points used for training. | | | The reason for this phenomenon is that the network "overfits" the data, i.e., the network tries to fit the noise in the data as well as the underlying function to be approximated. | | | Note that no attempt has been made to optimize the network size or the value of the learning rates. |
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http://neuron.eng.wayne.edu/bpFunctionApprox/bpFunctionApprox.html
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| | Neural Networks for Optimal Approximation of Smooth and Analytic Functions - Mhaskar (ResearchIndex) |
| | We prove that neural networks with a single hidden layer are capable of providing an optimal order of approximation for functions assumed to possess a given number of derivatives, if the activation function evaluated by each principal element satisfies certain technical conditions. | | | H.N. Mhaskar, "Neural Networks for Optimal Approximation of Smooth and Analytic Functions", to appear in Neural Computation, 1995. | | | 0.7: On the Near Optimality of the Stochastic Approximation of.. |
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http://citeseer.ist.psu.edu/mhaskar96neural.html
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| | David B. Shmoys: Selected Recent Publications |
| | In: Approximation Algorithms for Combinatorial Optimization, Lecture Notes in Computer Science 1444 (K. Jansen and J. Rolim, eds.), Springer, Berlin, 1998, 15-32. | | | In: Approximation Algorithms for Combinatorial Optimization, Lecture Notes in Computer Science 1913, (K. Jansen and S. Khuller, eds.), Springer, Berlin, 2000, 27-33. | | | "Sampling-based approximation algorithms for multi-stage stochastic optimization.".ps version To appear in FOCS 2005. |
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http://www.orie.cornell.edu/%7Eshmoys/publications.html
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| | Approximation Algorithms |
| | Approximation Algorithms for Bin Packing: A Survey, E. Coffman, Jr., M. Garey, and D. Johnson, Approximation Algorithms for NP-Hard Problems, D. Hochbaum (editor), PWS Publishing, Boston (1997), 46-93. | | | A chapter on the book "Approximation Algorithms for NP hard optimization problems". | | | Approximability of Optimization Problems, MIT, Fall 99 (Lecturer: Madhu Sudan) |
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http://www.csd.uwo.ca/~bma/teaching/approx/resources.html
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| | [No title] |
| | Approximation and online algorithms are fundamental tools used to deal with computationally hard problems and problems in which the input is gradually disclosed over time. | | | The proceedings of the workshop will be published as a volume in either the series Lecture Notes in Computer Science or Electronic Notes in Theoretical Computer Science. | | | An ARACNE mini-symposium on approximation and randomized algorithms in communication networks will take place as part of the workshop. |
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http://www.informatik.uni-kiel.de/inf/Jansen/conference/waoa03.html
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| | AFSJ - The approximation of European law |
| | The two processes must be conducted jointly but also autonomously, because mutual recognition and approximation pursue two different objectives. | | | They have so far addressed this question only on a case-by-case basis, approximating not the maximum sentences themselves, but only minimum levels for maximum sentences. | | | Mutual recognition has the goal of getting legal systems to coincide while safeguarding their diversity, whereas approximation seeks inversely to standardise these systems. |
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http://www.europarl.eu.int/comparl/libe/elsj/zoom_in/20_en.htm
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| | [No title] |
| | Approximation Algorithms for Data Placement on Parallel Disks. | | | Approximation Algorithms for the Largest Common Subtree Problem. | | | Approximation Algorithms for the Metric Labeling Problem via a New Linear Programming Formulation. |
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http://www.cis.upenn.edu/%7Esanjeev/pubs.html
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| | A 5/8 Approximation Algorithm for the Maximum Asymmetric TSP |
| | A 5/8 Approximation Algorithm for the Maximum Asymmetric TSP: SIAM Journal on Discrete Mathematics Vol. | | | This (1) improves upon the approximation factors of previous results and (2) presents a simpler solution to the previously fairly involved algorithms. | | | We propose a polynomial time approximation algorithm for the problem with a 5/8 approximation guarantee. |
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http://epubs.siam.org/sam-bin/dbq/article/40286
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| | PCP Links |
| | A survey of approximation algorithms for combinatorial optimization problems. | | | Indicates, for each problem, both the factor achieved by the best known approximation algorithm and the best known hardness result, with references to the relevant sources. | | | A comprehensive summary of the current approximability status of over 150 optimization problems. |
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http://www-cse.ucsd.edu/users/mihir/pcp.html
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| | Amazon.com: Books: Approximation 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. | | | Approximation Algorithms for NP-Hard Problems by Pws Pub Co | | | This book covers the dominant theoretical approaches to the approximate solution of hard combinatorial optimization and enumeration problems. |
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http://www.amazon.com/exec/obidos/tg/detail/-/3540653678?v=glance
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| | A More Efficient Approximation Scheme for Tree Alignment |
| | As in the existing PTASs in the literature, the basic approach of our algorithm is to partition the given tree into overlapping components of a constant size and then apply local optimization on each such component. | | | A More Efficient Approximation Scheme for Tree Alignment: SIAM Journal on Computing Vol. | | | Some experiments of the algorithm on simulated and real data are also given. |
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http://epubs.siam.org/sam-bin/dbq/article/31350
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| | Amazon.com: Books: Approximation Algorithms for NP-Hard Problems |
| | Developing approximation algorithms for NP hard problems is now a very active field in Mathematical Programming and Theoretical Computer Science. | | | Provides computer scientists and operations researchers with an effective framework for analyzing approximation algorithms and applying them to the solution of intractable problems. | | | With chapters contributed by leading researchers in the field, this book introduces unifying techniques in the analysis of approximation algorithms. |
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http://www.amazon.com/exec/obidos/tg/detail/-/0534949681?v=glance
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| | 6.893: Approximability of Optimization Problems |
| | Lecture 1 (9/8): Introduction to NP, NP Optimization, Approximation. | | | Preliminary version of a book on Approximation Algorithms by Rajeev Motwani, 1992. | | | For now here are some sources for approximation algorithms; and hardness of approximations. |
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http://theory.lcs.mit.edu/~madhu/FT99/course.html
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| | Rational Approximation Experiments |
| | Altho this formal transformation cannot add any information to the approximation, experimentally it appears that, for many functions, the Pade transformation of the Taylor or Chebyshev approximation is better than the original approximation. | | | Alternatively, it's possible that rational approximations are defective, and do not exist for many degrees. | | | Since the distribution of the error can also be interesting, for most methods, I will also plot the error between arcsin and the approximating function. |
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http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/arcsin
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| | Definition of Approximation |
| | Though our result is discouraging, we recall that the infinite limits approximation may in fact be simulated by using a different windowing function, as has been covered earlier. | | | Here, we consider why this is not valid for the rectangle window case. | | | Herein, we rigorously show why this is not a valid approach. |
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http://ccrma-www.stanford.edu/~asmaster/fresnelanalpaper/fresnelanal/node56.html
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| | APPROX 2002 Home Page |
| | The workshop on approximation algorithms for combinatorial optimization problems focuses on algorithmic and complexity aspects arising in the development of efficient approximate solutions to computationally difficult problems. | | | APPROX 2001, 4th International Workshop on Approximation Algorithms for Combinatorial Optimization, Berkeley, CA, USA, 2001. | | | International Workshop on Approximation Algorithms for Combinatorial Optimization |
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http://www.dis.uniroma1.it/~algo02/approx02
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| | Learning and Value Function Approximation in Complex Decision Processes |
| | Unfortunately, exact computation of the value function typically requires time and storage that grow proportionately with the number of states, and consequently, the enormous state spaces that arise in practical applications render the algorithms intractable. | | | We also present a computational case study involving a complex optimal stopping problem that is representative of those arising in the financial derivatives industry. | | | As a special case of temporal--difference learning in a context involving control, we propose variants of the algorithm that generate approximate solutions to optimal stopping problems. |
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http://web.cps.msu.edu/rlr/pub/VanRoy1.html
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| | Approximation Algorithms for NP-Hard Problems |
| | The approximation algorithms' framework provides a guarantee on the quality of the solution obtained. | | | Such problems are commonly addressed with heuristics that provide a solution, but not information on the solution's quality. | | | This framework has been used as a guide to developing algorithms in specific problem areas with increasingly improved performance. |
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http://www.ieor.berkeley.edu/~hochbaum/html/book-aanp.html
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| | Approximation |
| | If you estimate the position of the object by neglecting changes in velocity, then the result is a Linear Approximation to the true position function, and its graph is just the tangent line to the true graph. | | | The Differential and Tangent Line Approximations can be used to estimate experimental errors and to get approximate results for calculations that would be hard to do exactly. | | | (This should work because there are three conditions to match and a quadratic has three coefficients for us to choose.) And for even better approximations we might match higher derivatives by using higher degree polynomials. |
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http://www.langara.bc.ca/mathstats/resource/onWeb/calculus/approximation
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| | [No title] |
| | An optimal multilevel preconditioner for solenoidal approximations of the 2D-Stokes problem. | | | Greedy algorithms and best m-term approximation with respect to biorthogonal systems. | | | Optical filter architecture for approximating any 2 x 2 unitary matrix Optics Letters, vol. |
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http://www.faculty.iu-bremen.de/poswald
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| | Rectangle Window: Large Fresnel Integral Limits Approximation |
| | As we will see, this can in fact be done by choosing a different time domain windowing function. | | | We take a moment to consider consequences of this result. | | | Making this claim without actually using a longer window, however,is a mathematical disaster. |
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http://ccrma-www.stanford.edu/~asmaster/fresnelanalpaper/fresnelanal/node23.html
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| | MT A14303 |
| | In class we constructed the approximating polynomial from the values of | | | For a 17th degree approximation what is the error at 4? | | | What is the error at x0=2 with a 40th degree approximation? |
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http://www.slu.edu/classes/maymk/SeriesGraphs/SeriesNotes.html
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| | Approximation Theory |
| | Stahl, ``Simultaneous rational approximants to a Nikishin system of two functions''. | | | Research is planned on zero distribution via asymptotic methods of Hermite-Pade polynomials for the exponential function. | | | (xiii) K.A. Driver and H. Stahl, ``Simultaneous rational approximants to Nikishin systems of two functions''. |
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http://www.wits.ac.za/science/number_theory/pubat2.htm
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| | Lecture-notes: Approximation Algorithms for Network Problems |
| | Bicriteria approximation algorithms for network design problems basic notions, a general method for similar objectives, diameter-bounded minimum spanning trees | | | Minimum spanning trees optimality conditions, algorithms, LP formulation of Edmonds | | | Balanced separators of graphs Leighton-Rao algorithm for sparsest cuts and related topics |
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http://www.math.uwaterloo.ca/~jcheriya/lecnotes.html
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| | Michel X. Goemans |
| | Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques | | | Mathematics of Operations Research, Information and Computation and of the | | | Approximation Algorithms for MAX-3-CUT and Other Problems Via Complex Semidefinite Programming |
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http://www-math.mit.edu/~goemans
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| | definition of approximation |
| | The act of approximating; a drawing, advancing or being near; approach; also, the result of approximating. | | | Act, Advancing, Also, An, Approach, Approximating, Approximation, As, Being, But, By, Calculation, Coming, Conception, Continual, Correct, Drawing, Equation, Estimate, Etc, Exactly, Given, Is, Near, Nearer, Nearly, Not, Of, Or, Quality, Quantity, Result, Solve, That, The, To, Value | | | Act, Advancing, Also, An, Approach, Approximating, Approximation, As, Being, But, By, Calculation, Coming, Conception, Continual, Correct, Drawing, Equation, Estimate, Exactly, Given, Is, Near, Nearly, Not, Of, Or, Quality, Quantity, Result, Solve, That, The, To, Value |
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http://www.brainydictionary.com/words/ap/approximation131766.html
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| | Multivariate Approximation and Applications - Cambridge University Press |
| | Approximation theory in the multivariate setting has many applications including numerical analysis, wavelet analysis, signal processing, geographic information systems, computer aided geometric design and computer graphics. | | | Applied and computational aspects of nonlinear wavelet approximation A. Cohen; 8. | | | The field is fascinating since much of the mathematics of the classical univariate theory does not straightforwardly generalize to the multivariate setting, so new tools are required. |
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http://books.cambridge.org/0521800234.htm
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| | Vijay V. Vazirani |
| | ``Approximation Algorithms for Metric Facility Location and k-Median Problems Using the Primal-Dual Schema and Lagrangian Relaxation'', with K. Jain, Journal of ACM, Vol. | | | ``Recent Results on Approximating the Steiner Tree Problem and its Generalizations'', Theoretical Computer Science, Vol. | | | ``An Improved Approximation Scheme for Computing Arrow-Debreu Prices for the Linear Case'', with N. Devanur, Proc. |
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http://www.cc.gatech.edu/fac/Vijay.Vazirani
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| | Home Page for Andrzej Lingas |
| | The research is in part supported by the VR project "Efficient algorithms and approximation heuristics for combinatorial and geometric problems" and the ESPRIT project RAND-APX (Randomized and approximation algorithms). | | | The design and analysis of efficient sequential and parallel algorithms for combinatorial and geometric problems. | | | Polynomial-time approximation schemes for Euclidean minimum cost k-connectivity (geometric graph algorithms) |
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http://www.cs.lth.se/home/Andrzej_Lingas
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| | Decision Tree for Optimization Software -- Approximation |
| | Here a list of some representative approximation algorithms is given. | | | rational approximation to finite set of data (differential correction algorithm) | | | best polynomial approximation to a discrete one-dimensional data set in the Chebyshev (minimax) sense |
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http://plato.la.asu.edu/topics/problems/approx.html
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| | Australasian Approximation Theory People |
| | Approximation and interpolation of nonlinear operators in the modelling of dynamical systems, matrix approximation theory and algorithms, radial basis functions, sigmoidal functions etc | | | Numerical approximation, smoothing splines, fast algorithms for radial basis functions, inverse problems, image processing | | | Fast algorithms and error estimates for radial basis functions (applications to image processing and natural resource modelling) |
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http://www.math.auckland.ac.nz/~waldron/NZATG/australasians.html
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| | Overview of Computational Chemistry |
| | The Born-Oppenheimer approximation is the first of several approximations made when trying to solve Schroëdinger's equation for more complex systems than one or two electrons. | | | In order to be able to solve Schroëdinger's equation for any system larger than an atom with one electron, various approximations need to be made. | | | It separates electron and nuclear motion based on the idea that nuclear mass is so much larger than electron mass that the nuclei are basically "fixed" particles. |
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http://www.shodor.org/chemviz/overview/boa.html
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| | SurfStat.australia |
| | For accurate values for binomial probabilities, either use computer software to do exact calculations or if n is not very large, the probability calculation can be improved by using the continuity correction. | | | Hence, if X has the binomial distribution ie. | | | When an outcome X needs to be included in the probability calculation, the normal approximation uses the interval from (X-0.5) to (X+0.5). |
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http://www.anu.edu.au/nceph/surfstat/surfstat-home/3-2-8.html
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| | Amazon.ca: Books: Theory of Approximation |
| | 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 applications to turbulence, chaos and fractals; computational efficiencies from scaling similarities, and data compression; and new adaptive non-linear algorithms. | | | An Example of Approximating with the Aid of Periodic Functions | | | This should be on the reading list of every graduate student in control or signal processing. |
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http://www.amazon.ca/exec/obidos/ASIN/0486671291
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| | Carl de Boor's Home Page |
| | Approximation and Computation (DeVore Fest), South Carolina, 12-17may01 (here are some pictures) | | | Check out the latest versions of the various programs and drivers in that last book. | | | Ditto for Constructive Approximation (published by Springer-Verlag () which publishes many other journals). |
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http://www.cs.wisc.edu/~deboor
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| | Approximation Algorithms |
| | By this lecture, you will know the linear programming method in approximation algorithm design. | | | graph matching and a ratio 2 approximation for Vertex Cover; | | | This lecture gives a PTAS -- the best you can do to an NP-hard optimization problem. |
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http://www.csd.uwo.ca/faculty/bma/teaching/approx/schedule.html
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