61. The Use Of Padé Approximation To Eliminate Nonuniformities Of Your browser may not have a PDF reader available. Google recommends visiting our text version of this document. http://www.springerlink.com/index/M53H327601306477.pdf

62. Wiley InterScience :: Session Cookies Your browser may not have a PDF reader available. Google recommends visiting our text version of this document. http://doi.wiley.com/10.1002/qua.560440829

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63. First Steps In Numerical Analysis Note that this expansion has only oddpowered terms so, although the polynomial approximation is of degree (2k - 1 ), it has only k terms. http://mpec.sc.mahidol.ac.th/numer/STEP5.HTM

STEP 5 ERRORS 5 Approximation to functions An important procedure in Analysis is to represent a given function as an infinite series of terms involving simpler or otherwise more appropriate functions. Thus, if f is the given function, it may be represented as the series expansion involving the set of functions . Mathematicians have spent a lot of effort in discussing the convergence of series, i.e., on defining conditions for which the partial sum approximates the function value f (x) ever more closely as n increases. In Numerical Analysis, we are primarily concerned with such convergent series; computation of the sequence of partial sums is an approximation process in which the truncation error may be made as small as we please by taking sufficient terms into account. The Taylor series The most important expansion to represent a function is the Taylor series. If f is suitably smooth in the neighbourhood of some chosen point x we have where h = x - x denotes the displacement from x to the point x in the neighbourhood, and the rcmainder term is

64. Chicago Journals - The Astrophysical Journal Indeed, it is as important that a good approximation can be obtained when the expansion is truncated after a small number of terms as it is for the http://www.journals.uchicago.edu/cgi-bin/resolve?1997ApJ...483..464L

65. Approximation Inference (SNN Nijmegen) This approximation, which has its origin in statistical physics, can be viewed as a first order expansion around the ultimate tractable distribution the http://www.snn.ru.nl/nijmegen/approx-graph.php3

Approximation Inference Approximation Methods for Graphical Models People involved: Martijn Leisink (contact person), Wim Wiegerinck, Kees Albers, Bert Kappen (supervisor). Duration: January 1998 until February 2005. Funding: STW Pionier. The aims of this project are to develop novel approximation methods for learning and inference in complex probability models. Inference is the problem to compute marginal probabilities given a probability model. Learning is the problem to estimate model parameters from data. The learning problem contains in general the inference problem as a subtask. A major problem in probabilistic modelling with many variables is the computational complexity involved in typical calculations for inference. For sparsely connected probabilistic networks this problem has been solved during the last decades by the invention of efficient algorithms for exact inference. However, in large, densely connected models exact inference is intractable . This means that the computation time increases exponentially with the problem size. In such a case, sampling methods, like Markov Chain Monte Carlo (MCMC) may seem a straightforward solution, but may require extreme long computation time to gather a sufficient amount of samples. An alternative solution is provided by variational methods. These methods do the approximations directly by fitting distributions rather than by gathering statistics from samples. Basically, variational methods expand the intractable distribution around an approximate distribution that is tractable. One of the simplest and most prominent variational approximations is the so-called mean field approximation. This approximation, which has its origin in statistical physics, can be viewed as a first order expansion around the ultimate tractable distribution: the one in which all variables are decoupled.

66. Komatsu: On Inhomogeneous Diophantine Approximation With Some Quasi-periodic Exp 5 T. Komatsu On inhomogeneous continued fraction expansion and inhomogeneous Diophantine approximation. J. Number Theory 62 (1997), 192212. http://jtnb.cedram.org/jtnb-bin/fitem?id=JTNB_1999__11_2_331_0

67. Neural Comp. -- Sign In Page Using perturbation expansion of the Kullback divergence (or Plefka expansion in statistical physics), a formulation of meanfield approximation of general http://neco.mitpress.org/cgi/content/full/12/8/1951

HOME HELP FEEDBACK SUBSCRIPTIONS ... SEARCH QUICK SEARCH: [advanced] Author: Keyword(s): Year: Vol: Page: This item requires a subscription to Neural Computation Online. Full Text Information Geometry of Mean-Field Approximation Tanaka Neural Comp.. To view this item, select one of the options below: Sign In User Name Sign in without cookies. Can't get past this page? Help with Cookies. Need to Activate? Password Forgot your user name or password? Sign Up Subscribe to the Journal - Subscribe to the print and/or online journal. This Article Abstract Full Text (PDF) Alert me when this article is cited ... Alert me if a correction is posted Services Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Tanaka, T. Search for Related Content PubMed PubMed Citation Articles by Tanaka, T. HOME HELP ... J COGNITIVE NEUROSCIENCE NEURAL COMPUTATION MIT PRESS JOURNALS

68. Taylor Series derivative approximation. gradient approximation. gradientHessian approximation. Taylor polynomial. Taylor series expansion http://riskglossary.com/articles/taylor_series.htm

Taylor Series Expansion Explained: derivative approximation gradient approximation gradient-Hessian approximation Taylor polynomial ... Ads by Contingency Analysis Polynomials are frequently used to locally approximate functions. There are various ways this may be done. This article discusses several forms of differential approximation, culminating with Taylor series. Univariate Approximations Consider a function f that is differentiable in an open interval about some point The linear polynomial is called a derivative approximation . It provides a good approximation for f , at least in a small interval about . This is because: equals f at , and has the same first derivative as f at If f is twice differentiable in an open interval about , we can improve the approximation with a quadratic polynomial Consider the function which has first and second derivatives on . Let’s construct a linear polynomial approximation for f about the point = 0. Applying [

69. Faculty_profile Dielectric response of solid state plasmas; random phase approximation; of periodic lattice in the harmonic approximation, eigenvector expansion of http://www.stevens.edu/ses/about_soe/faculty/faculty_profile.php?faculty_id=437

70. CJO - Abstract - Estimates Of The Errors Incurred In Various Asymptotic Represen Your browser may not have a PDF reader available. Google recommends visiting our text version of this document. http://journals.cambridge.org/production/action/cjoGetFulltext?fulltextid=389738

71. AN EXPANSION FORMULA FOR THE DRAG ON A CIRCULAR CYLINDER MOVING Your browser may not have a PDF reader available. Google recommends visiting our text version of this document. http://qjmam.oxfordjournals.org/cgi/reprint/4/4/401.pdf

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