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41: Approximations And Expansions
Introduction. approximations and expansions primarily concern the approximationof classes of real functions by functions of special types.
http://www.math.niu.edu/~rusin/known-math/index/41-XX.html

Extractions: POINTERS: Texts Software Web links Selected topics here Approximations and expansions primarily concern the approximation of classes of real functions by functions of special types. This includes approximations by linear functions, polynomials (not just the Taylor polynomials), rational functions, and so on; approximations by trigonometric polynomials is separated into Fourier analysis (below). Topics include criteria for goodness of fit, error bounds, stability upon change of approximating family, and preservation of functional characteristics (e.g. differentiability) under approximation. Effective techniques for specific kinds of approximation are also prized. This is also the area covering interpolation and splines. For all approximation theory in the complex domain, See 30Exx, 30E05, and 30E10; for all trigonometric approximation and interpolation, see 42Axx, 42A10, and 42A15; for numerical approximation, See 65Dxx This image slightly hand-edited for clarity.
Limit, Expansions And Approximations Of The Posterior Distribution
Limit, expansions and approximations of the posterior distribution In Bayesian inference, one looks at the posterior distribution for the purpose of making inference.
http://www.cs.vu.nl/~ghosal/post.html

Extractions: In Bayesian inference, one looks at the posterior distribution for the purpose of making inference. It is thus necessary to have certain reasonable large sample behaviour of the posterior distribution. The foremost concern is consistency. In parametric problems, both regular and non-regular, one virtually always has consistency for almost any reasonable prior. Moreover, the posterior converges at the best possible rate. One particular consequence of consistency is that the posteriors, based on two different priors, are much the same for large enough sample sizes. For more details, please look at our papers in Statistical Decision Theory and Related Fields V (S. S. Gupta and J. O. Berger, eds.), pp. 183-199, 1994 and The Annals of Statistics 23, pp. 21452152, 1995, and the references mentioned there. For non-parametric (and semi-parametric) problems, consistency is much more non-trivial and can hold only for some nice priors. See the page Nonparametric Bayesian inference for details.
Approximations And Expansions
approximations and expansions 41Axx approximations and expansions
http://www.iwr.uni-heidelberg.de/groups/compalg/gruber/WWW/41-XXmon.html
Index Via Los Alamos Preprint Hierarchy System
Special functions, orthogonal polynomials, harmonic analysis, ODEs, differentialrelations, calculus of variations, approximations, expansions, asymptotics;
http://www.math.niu.edu/~rusin/known-math/index/LANL.html

Extractions: Search Subject Index MathMap Tour ... Help! Here are the subdivisions of mathematics classified according to the system used at the Los Alamos preprint-server. The LANL archive is largely an amalgam of independently-founded specialty archives, and thus is not necessarily comprehensive in scope nor non-duplicative nor arranged according to any single system. (Other specialty preprint servers are mentioned on the corresponding index pages at this site.) We provide links here to what appear to be the best-matching index pages at this site to each of the 31 subject classes at LANL. You can go directly back to the index arranged according to the AMS/Zbl Mathematics Subject Classification system used to organize materials at this site. There are also separate categories at LANL for Computer Science Physics , and "Nonlinear Sciences" [Adaptation, Noise, and Self-Organizing Systems / Chaotic Dynamics / Cellular Automata and Lattice Gases / Nonlinear Sciences / Pattern Formation and Solitons / Exactly Solvable and Integrable Systems ] The remainder of this page is taken nearly verbatim from http://xxx.lanl.gov/new/math.html
Notes On Binomial Expansions And Approximations*
Notes on Binomial expansions and approximations Notes on Binomial expansions and approximations* You should know that there is a general way to calculate out the coefficients of the following expression (a + b) b + n(n1)
http://www.haverford.edu/physics-astro/MathAppendices/Binomial_Expansions.pdf
KLUWER Academic Publishers | Approximations And Expansions
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http://www.wkap.nl/home/topics/J/5/1/
Quadrature Formulae And Asymptotic Error Expansions For Wavelet Approximations O
Quadrature Formulae And Asymptotic Error expansions For Wavelet approximations Of Smooth Functions (1994) (Make
http://citeseer.nj.nec.com/sweldens94quadrature.html

Extractions: Abstract: . This paper deals with typical problems that arise when using wavelets in numerical analysis applications. The first part involves the construction of quadrature formulae for the calculation of inner products of smooth functions and scaling functions. Several types of quadratures are discussed and compared for different classes of wavelets. Since their construction using monomials is ill-conditioned, also a modified, well-conditioned construction using Chebyshev polynomials is presented. The... (Update)
KLUWER Academic Publishers | Approximations And Expansions
The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet approximations AbdulJ. Jerri August 1998, ISBN 07923-5109-6, Hardbound Price 172.50 EUR
http://www.wkap.nl/home/topics/J/5/1/?sort=Z&results=0
REGULAR ARTICLES Exponential Asymptotic Expansions And Approximations
Exponential asymptotic expansions and approximations of the unstable and stable manifolds of singularly perturbed systems with the He´non map as an example Department of Mathematics, University of Central Florida, Orlando, Florida 328161364
http://www.chem.wvu.edu/cjaffe/Publications/chaos_1998.pdf
Approximations And Expansions
browsing 'approximations and expansions' Related Collections. Browse Help.Fully equivalent approximations and expansions (41-XX) Minor
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About "Approximations And Expansions"
approximations and expansions Visit this site edu/~ rusin/ known math/ index/ 41- XX. Dave Rusin; The Mathematical Atlas
http://mathforum.com/library/view/7602.html

Extractions: Visit this site: http://www.math.niu.edu/~rusin/known-math/index/41-XX.html Author: Dave Rusin; The Mathematical Atlas Description: A short article designed to provide an introduction to approximations and expansions, which primarily concern the approximation of classes of real functions by functions of special types. This includes approximations by linear functions, polynomials (not just the Taylor polynomials), rational functions, and so on; approximations by trigonometric polynomials is separated into Fourier analysis (below). Topics include criteria for goodness of fit, error bounds, stability upon change of approximating family, and preservation of functional characteristics (e.g. differentiability) under approximation. Effective techniques for specific kinds of approximation are also prized. This is also the area covering interpolation and splines. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. Levels: College Languages: English Resource Types: Articles Math Topics: Approximation/Expansion
Renardus Search Results
Subject, 41XX approximations and expansions (MSC2000); 65-XX Numerical analysis(MSC2000); 31.49 Analysis Sonstiges (BK); University of Erlangen-Nuremburg
http://www.renardus.org/cgi-bin/egwcgi/egwirtcl/screen.tcl/name=ShowHits&lang=en
About "Approximations And Expansions"
approximations and expansions. Library Home Full Table of Contents Suggest a Link Library Help Visit this site http//www
http://mathforum.org/library/view/7602.html

Extractions: Visit this site: http://www.math.niu.edu/~rusin/known-math/index/41-XX.html Author: Dave Rusin; The Mathematical Atlas Description: A short article designed to provide an introduction to approximations and expansions, which primarily concern the approximation of classes of real functions by functions of special types. This includes approximations by linear functions, polynomials (not just the Taylor polynomials), rational functions, and so on; approximations by trigonometric polynomials is separated into Fourier analysis (below). Topics include criteria for goodness of fit, error bounds, stability upon change of approximating family, and preservation of functional characteristics (e.g. differentiability) under approximation. Effective techniques for specific kinds of approximation are also prized. This is also the area covering interpolation and splines. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. Levels: College Languages: English Resource Types: Articles Math Topics: Approximation/Expansion
The Math Forum - Math Library - Approximtn/Expnsn
approximations and expansions Dave Rusin; The Mathematical Atlas A short articledesigned to provide an introduction to approximations and expansions, which
http://mathforum.org/library/topics/approx_expand/

Extractions: A short article designed to provide an introduction to approximations and expansions, which primarily concern the approximation of classes of real functions by functions of special types. This includes approximations by linear functions, polynomials (not just the Taylor polynomials), rational functions, and so on; approximations by trigonometric polynomials is separated into Fourier analysis (below). Topics include criteria for goodness of fit, error bounds, stability upon change of approximating family, and preservation of functional characteristics (e.g. differentiability) under approximation. Effective techniques for specific kinds of approximation are also prized. This is also the area covering interpolation and splines. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. more>>
Stochastic Expansions And Asymptotic Approximations.
Author(s) Magdalinos, Michael A Abstract No abstract available
http://netec.wustl.edu/BibEc/data/Articles/cupetheorv:8:y:1992:i:3:p:343-67.html
Taylor Series Expansions And Approximations
Taylor Series expansions and approximations The Taylor series is mainly used for approximating functions when one can identify a small parameter. Expansion techniques are useful for many
http://www.haverford.edu/physics-astro/MathAppendices/Taylor_Series.pdf
Elementary Expansions, Limits Approximations
Next About this document Up SOME HANDY MATH Previous Central Limit Theorem.Elementary expansions, Limits approximations. Assume throughout that .
http://musr.physics.ubc.ca/~jess/p455/math/node4.html
Papers By AMS Subject Classification
41XX approximations and expansions For all approximation theory in the complexdomain, see 30EXX 30E05 and 30E10 ; for all trigonometric approximation and
http://im.bas-net.by/mathlib/en/ams.phtml?parent=41-XX
[41Xxx] -- Approximations And Expansions
41Xxx approximations and expansions 41A17 . Inequalities inapproximation (Bernstein, Jackson, Nikolprime skiitype inequalities).
http://jipam.vu.edu.au/subj_classf/41Xxx.htm

Extractions: Approximations and Expansions Inequalities in approximation (Bernstein, Jackson, Nikolprime skii-type inequalities) Padé approximation Rate of convergence, degree of approximation Approximation by other special function classes Best approximation, Chebyshev systems Approximate quadratures Miscellaneous topics Editors R.P. Agarwal
Preprint 1998 Mathematik HUB
Quantization of the MICKepler Problem PREPRINT 98-13 Dentcheva, Darinka approximations,expansions and Univalued Representations of Multifunctions PREPRINT 98
http://www.mathematik.hu-berlin.de/publ/pre/1998/p-list-98.html

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