41. Analytical Approximations Of Fractional Delays: Lagrange Interpolators And Allpa by approximating the ideal Fourier transform of the fractional delay according totwo different Padé approximations series expansions and continued fraction http://www.ircam.fr/equipes/analyse-synthese/tassart/these/icassp97/article.html

Next: Introduction S. Tassart, Ph. Depalle IRCAM, Analysis/Synthesis Team 1 place Igor-Stravinsky, 75004 PARIS, FRANCE tassartircam.fr, phdircam.fr Analytical Approximations of Fractional Delays: Lagrange Interpolators and Allpass Filters Abstract: Introduction Ideal Fractional Delay From Continuous to Discrete An Ideal Transfer Function ... About this document ... Stephan Tassart Wed May 21 17:49:28 MET DST 1997

42. Linearized Approximations Linearized approximations. Because p x (the zerooffset slope) is typically lowerthan (the migrated slope), we perform initial expansions in terms of y=p x v http://sepwww.stanford.edu/public/docs/sep94/tariq3/paper_html/node10.html

Next: About this document ... Up: Alkhalifah and Fomel: Anisotropy Previous: Relating the zero-offset and Linearized approximations Although the exact expressions might be sufficiently constructive for actual residual migration applications, linearized forms are still useful, because they give us valuable insights into the problem. The degree of parameter dependency for different reflector dips is one of the most obvious insights in the anisotropy continuation problem. Perturbation of a small parameter provides a general mechanism to simplify functions by recasting them into power-series expansion over a parameter that has small values. Two variables can satisfy the small perturbation criterion in this problem: The anisotropy parameter ) and the reflection dip or p x v Setting yields equation ( ) for the velocity continuation in elliptical anisotropic media and which represents the case when we initially introduce anisotropy into our model. Because p x (the zero-offset slope) is typically lower than (the migrated slope), we perform initial expansions in terms of

43. 1 Introduction appeared for functions of a single variable in the form of minimax polynomial orrational approximations, or truncated Chebyshevseries expansions; see, for http://gams.nist.gov/mcsd/Reports/2001/nesf/node2.html

Next: 2 Mathematical Developments Up: Numerical Evaluation of Special Previous: Contents 1 Introduction continues to be one of the best-selling mathematical books of all time The purpose of the present paper is to provide some assistance to those mathematicians, engineers, scientists, and statisticians who discover that they need to generate numerical values of the special functions in the course of solving their problems. ``Generate'' is the operative word here: we are thinking primarily of either software or numerical approximations that can be programmed fairly easily. Numerical tables are not covered in this survey. Furthermore, for the most part we shall concentrate on the functions themselves; only in certain cases do we include, for example, zeros, inverse functions or indefinite integrals. Elementary functions, also, are excluded . Lastly, we believe that the majority of readers would prefer us to emphasize the more useful algorithms rather than make an attempt to be encyclopedic: algorithms or approximations that have clearly been superseded are omitted. We identify three stages in the development of computational procedures for the special functions: Derivation of relevant mathematical properties.

44. DIFFERENCE APPROXIMATIONS AT INTERNAL PHYSICAL BOUNDARIES Existence of asymptotic expansions for discretization error and their use in errorestimation is studied in the light of approximations of the resulting http://www.worldscinet.com/ijmpc/08/0806/ali.html

International Journal of Modern Physics C, Vol. 8, No. 6 (1997) 1267-1285 DIFFERENCE APPROXIMATIONS AT INTERNAL PHYSICAL BOUNDARIES FARHAD ALI Dr. A. Q. Khan Research Laboratories, P. O. Box 502, Rawalpindi, Pakistan E-mail Two sample difference approximations at internal physical boundaries, in magnetic field calculations, are analyzed in the light of truncation and discretization error expansions. Existence of asymptotic expansions for discretization error and their use in error estimation is studied in the light of approximations of the resulting variational equations. Two test problems are presented to illustrate validity of the error analysis. Better difference approximations are shown to lead to better approximation of the associated variational equations. Keywords : Internal Boundaries; Magnetostatic Potential; Difference Approximation; Truncation and Discretization Errors; Asymptotic PDF SOURCE Back to Contents of Vol. 8, No. 6

45. Browse MSC2000 Scheme, 41XX. approximations and expansions. For etc. 41-99, approximationsand expansions not classified at a more specific level, 41A05, http://www.zblmath.fiz-karlsruhe.de/MATH/msc/zbl/msc/2000/41-XX/dir

Contact Search Browse Instructions ... Main Changes 70th anniversary Zentralblatt MATH Home Facts and Figures Partners and Projects Subscription Service Database Gateway Database Mirrors Reviewer Service Classification ... Serials and Journals database Miscellanea Links to the Mathematical World Display Text version Printer friendly page Internal Browse MSC2000 - by section and classification TOP MSC2000 - Mathematics Subject Classification Scheme 41-XX Approximations and expansions [For all approximation theory in the complex domain, see and ; for all trigonometric approximation and interpolation, see and ; for numerical approximation, see Classification Topic X-ref General reference works handbooks, dictionaries, bibliographies, etc. Instructional exposition textbooks, tutorial papers, etc. Research exposition monographs, survey articles Historical must also be assigned at least one classification number from Section 01 Explicit machine computation and programs not the theory of computation or programming Proceedings, conferences, collections, etc.

46. Browse MSC2000 Mathematics Subject Classification Scheme Section 41XX approximations and expansionsFor all approximation theory in the complex domain, see 30Exx, 30E05 http://www.zblmath.fiz-karlsruhe.de/MATH/text/msc/zbl/msc/2000/41-XX/dir

ZENTRALBLATT MATH Home Facts and Figures Partners and Projects Subscription ... Graphical Version of this page. Browse MSC2000 - by section and classification Search Browse the MSC2000 by Classification]-[ Instructions for using the classification]-[ Main Changes from MSC1991 to MSC2000] TOP MSC2000 - Mathematics Subject Classification Scheme Section: 41-XX Approximations and expansions [For all approximation theory in the complex domain, see and ; for all trigonometric approximation and interpolation, see and ; for numerical approximation, see 41-00 General reference works handbooks, dictionaries, bibliographies, etc. 41-01 Instructional exposition textbooks, tutorial papers, etc. 41-02 Research exposition monographs, survey articles

47. Asymptotic Methods In Statistical Inference Download (PostScript format),; Chapter 3 Edgeworth expansions. First sectioncontaining the Edgeworth approximations. Download (PostScript format). http://www.dina.dk/~ib/asymp/plan.html

Asymptotic methods in statistical inference NB - new time and place Mondays 12.15 - 14.00 in Aud. 3-07. Course plan The course plan below shows the tentative content of each of the mondays. No doubt this will change as the course progresses, and the final part of the course will depend on the participants. First time is August 30. October 18 is cancelled (vacation) and so is November 8. 30/8-99. Introduction. From the likelihood equation to probability statements. Mathematical foundation (1): Asymptotic expansions, the order symbols, multilinear algebra. 13/9-99. Mathematical foundation (2): Differentials. 20/9-99. Mathematical foundation (3): Moments and cumulants. The saddlepoint approximation (via exponential tilting). 27/9-99. Laplace integration (1): Watson's lemma and extensions. 4/10-99. Laplace integration methods (ctd), uniform expansions, tail integrals. 11/10-99. Transformations of densities between surfaces, (the p-star formula). 18/10-99. VACATION 25/10-00. Inversion integrals and Edgeworth expansions for densities (and cdf's). 1/11-99. The delta method, cumulant computations, (marginal distributions).

48. Cluster Expansions For The Deterministic Computation Of Bayesian Estimators Base pp. 275293 Cluster expansions for the Deterministic Computation of Bayesian PeterC. Doerschuk Abstract—We describe a family of approximations, denoted by http://www.computer.org/tpami/tp1995/i0275abs.htm

March 1995 (Vol. 17, No. 3) p p. 275-293 Cluster Expansions for the Deterministic Computation of Bayesian Estimators Based on Markov Random Fields Chi-hsin  Wu, Peter C.  Doerschuk Abstract—We describe a family of approximations, denoted by “cluster approximations,” for the computation of the mean of a Markov random field (MRF). This is a key computation in image processing when applied to the a posteriori MRF. The approximation is to account exactly for only spatially local interactions. Application of the approximation requires the solution of a nonlinear multivariable fixed-point equation for which we prove several existence, uniqueness, and convergence-of-algorithm results. Four numerical examples are presented, including comparison with Monte Carlo calculations. Index Terms- Markov random fields, image restoration, Bayesian estimation, thresholded posterior mean estimator. The full text of IEEE Transactions on Pattern Analysis and Machine Intelligence is available to members of the IEEE Computer Society who have an online subscription and a web account

49. Application Of Vector-Valued Rational Approximations To The Matrix Eigenvalue Pr of these theorems it was shown how optimal approximations to the poles of $F(z)$and the principal parts of the corresponding Laurent series expansions can be http://epubs.siam.org/sam-bin/dbq/article/24316

SIAM Journal on Matrix Analysis and Applications Volume 16, Number 4 pp. 1341-1369 Application of Vector-Valued Rational Approximations to the Matrix Eigenvalue Problemand Connections with Krylov Subspace Methods Avram Sidi Abstract. J. Approx. Theory Key words. Krylov subspace methods, method of Arnoldi, method of Lanczos, power iterations, generalized power methods, diagonalizable matrices, defective matrices, eigenvalues, invariant subspaces, vector-valued rational approximations AMS Subject Classifications No full text available for this article. For additional information contact service@siam.org

50. An Alternative Approach To Obtaining Nagar-Type Moment Approximations In Sumulta While the expansions are essentially equivalent to the traditional Nagartupe,the terms are expressed in a form which enables moment approximations to be http://ideas.repec.org/p/fth/exetec/99-05.html

This file is part of IDEAS , which uses RePEc data Papers Articles Software Books ... Help! An Alternative Approach to Obtaining Nagar-Type Moment Approximations in Sumultaneous Equation Models Author info Abstract Publisher info Related research ... Statistics Author Info Phillips, G.D.A. Abstract The paper examines asymptotic expansions for estimation errors expressed explicitly as functions of unferlying random variables. Taylor series expansions are obtained from which first and secomd moment approximationc are derived. While the expansions are essentially equivalent to the traditional Nagar-tupe, the terms are expressed in a form which enables moment approximations to be obtained in a particular straightforward way, once the partial derivatives have been found. The approach is illustrated by considering the k-class estimators in a static simultaneous equation model where the distrubances are non-spherical. Publisher Info Paper provided by University of Exeter, School of Business and Economics in its series Discussion Papers with number 99/05. Length: 28 pages Date of creation: Date of revision: Handle: RePEc:fth:exetec:99/05 Keywords: REGRESSION ANALYSIS ; ECONOMETRICS

51. Robert Harlander: Aymptotic Expansions Padé approximations (for singlet diagrams). (For a review on Padé approximationssee here.) The results obtained through asymptotic expansions can be combined http://rharland.home.cern.ch/rharland/research/lmp.html

Robert Harlander CERN Theory Group CERN Research interests: Quark mass effects in higher order QCD - Asymptotic Expansions Asymptotic expansions A central part of my Ph.D. thesis was concerned with the precise determination of the influence of finite quark masses to the hadronic cross section at electron-positron colliders. A powerful tool for this kind of calculations is provided by the method of asymptotic expansion , an effective re-formulation of the operator product expansion (for a review see ). Previously, the application of this procedure was restricted to lower orders of perturbation theory because it requires the evaluation of the huge number of diagrams generated by this approach. Therefore we automated the method which allowed to compute the third order QCD corrections to the hadronic R ratio as an expansion in the quark mass (for a review on the automatic computation of Feynman diagrams, see Subdiagrams of the non-planar three-loop diagram that contribute to the large momentum procedure (taken from Top quark production at a Linear Collider It turned out that using the same strategy one could also examine top quark pair production at a linear collider. If the energy is slightly above the threshold region (click

52. EconPapers: Asymptotic Expansions For Some Semiparametric Program Evaluation Est We investigate the performance of a class of semiparametric estimators of the treatmenteffect via asymptotic expansions. We derive approximations to the first http://econpapers.hhs.se/paper/ifscemmap/04_2F01.htm

Asymptotic expansions for some semiparametric program evaluation estimators No CWP04/01 in CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies Hidehiko Ichimura and Oliver Linton lintono@lse.ac.uk Abstract: We investigate the performance of a class of semiparametric estimators of the treatment effect via asymptotic expansions. We derive approximations to the first two moments of the estimator that are calid to 'second order'. We use these approximations to define a method of bandwidth selection. We also propose a degrees of freedom like bias correction that improves the second order properties of the estimator but without requiring estimation of the higher order derivatives of the unknown propensity score. We provide some numerical calibrations of the results. Keywords: Bandwidth selection kernel estimation program evaluation semiparametric estimation ... treatment effect. (search for similar items in EconPapers) JEL-codes: (search for similar items in EconPapers) Date: Downloads: http://cemmap.ifs.org.uk/docs/cwp0401.pdf

53. New Books Author Index Subject Index Series Index Asymptotic approximations of Integrals contains the distributional method, whichis not in the general theory of asymptotic expansions, including smoothing http://ec-securehost.com/SIAM/CL34.html

new books author index subject index series index Purchase options are located at the bottom of the page. The catalog and shopping cart are hosted for SIAM by EasyCart. Your transaction is secure. If you have any questions about your order, contact harris@siam.org Asymptotic Approximations of Integrals R. Wong Classics in Applied Mathematics 34 Asymptotic methods are frequently used in many branches of both pure and applied mathematics, and this classic text remains the most up-to-date book dealing with one important aspect of this area, namely, asymptotic approximations of integrals. In Asymptotic Approximations of Integrals , all results are proved rigorously, and many of the approximation formulas are accompanied by error bounds. A thorough discussion on multidimensional integrals is given, and references are provided. Asymptotic Approximations of Integrals contains the "distributional method," which is not available elsewhere. Most of the examples in this text come from concrete applications. Since its publication twelve years ago, significant developments have occurred in the general theory of asymptotic expansions, including smoothing of the Stokes phenomenon, uniform exponentially improved asymptotic expansions, and hyperasymptotics. These new concepts belong to the area now known as "exponential asymptotics." Expositions of these new theories are available in papers published in various journals, but not yet in book form.

54. Generalized Poisson Models And Their Applications In Insurance And Finance: Cont formula for the ruin probability in the classical risk process approximations forthe ruin probability with small safety loading Asymptotic expansions for the http://www.vsppub.com/books/mathe/cbk-GenPoiModtheAppInsFin.html

Generalized Poisson Models and their Applications in Insurance and Finance Modern Probability and Statistics Contents: Foreword Preface BASIC NOTIONS OF PROBABILITY THEORY Random variables, their distributions and moments Generating and characteristic functions Random vectors. Stochastic independence Weak convergence of random variables and distribution functions Poisson theorem Law of large numbers. Central limit theorem. Stable laws The Berry-Esseen inequality Asymptotic expansions in the central limit theorem Elementary properties of random sums Stochastic processes POISSON PROCESS The definition and elementary properties of a Poisson process Poisson process as a model of chaotic displacement of points in time The asymptotic normality of a Poisson process Elementary rarefaction of renewal processes CONVERGENCE OF SUPERPOSITIONS OF INDEPENDENT STOCHASTIC PROCESSES Characteristic features of the problem Approximation of distributions of randomly indexed random sequences by special mixtures The transfer theorem. Relations between the limit laws for random sequences with random and non-random indices Convergence of distributions of randomly indexed sequences to identifiable location or scale mixtures. The asymptotic behavior of extremal random sumsNecessary and sufficient conditions for the convergence of distributions of random sequences with independent random indices

55. Approximation: Theory And Applications Numerische Mathematik; Foundations of Computational Mathematics; 2000Mathematics Subject Classification approximations and expansions. http://www.fi.uib.no/~antonych/Approx.html

Constructive Approximation Links to CA Problems Approximation Theory and its Applications ... Learning Evaluation Functions GAMS (Generalized Algebraic Modeling System) Development Corporation Model Library Subject Index: Agricultural Economics Applied General Equilibrium Modeling Chemistry and Chemical Engineering ... MobiDK: Ministry of Business and Industry, Model for Denmark Mathematical and Computational Science Division, Information Technology Laboratory, National Institute of Standards and Technology Guide to Available Mathematical Software Catalog of Algorithms for Approximation Problem Decision Tree Linear Algebra ... Virtual Pro, Inc.: Programming resources of Russia Can an approximation in multidimensional spaces be constructive indeed And what's about approximation of gradients/Hessians/etc., when a smooth function is given by a finite set of values corrupted with uncorrelated noise The Brachistochrone Challenge "I, Johann Bernoulli, greet the most clever mathematicians in the world. Nothing is more attractive to intelligent people than an honest, challenging problem whose possible solution will bestow fame and remain as a lasting monument. Following the example set by Pascal, Fermat, etc., I hope to earn the gratitude of the entire scientific community by placing before the finest mathematicians of our time a problem which will test their methods and the strength of their intellect. If someone communicates to me the solution of the proposed problem, I shall then publicly declare him worthy of praise."

56. Global-Investor Bookshop : Numerical Solution Of Stochastic Differential Equatio Convergence of Truncated StratonovichTaylor expansions 210 5.11 Weak Convergenceof Trunca ted Ito-Taylor expansions 211 5.12 Weak approximations of Multiple http://books.global-investor.com/books/15605.htm

home about us contact us Search all resources Books Conferences Exam courses Freebies Glossary In-house training Training courses global-investor Books Books Numerical Solution of Stochastic Differential Equations by P. Kloeden and E. Platen Search Bestsellers New books Bargains ... Shopping basket Numerical Solution of Stochastic Differential Equations by P. Kloeden and E. Platen Our price: You save Our reference code: 15605 ISBN: 3540540628 Published by Springer Verlag 3rd edition, published in 1999 632 pages, Hb [ Jacket Text ] [ Contents ] Jacket Text Contents Suggestions for the Reader xvii Basic Notation xxi Brief Survey of St ochastic Numerical Methods xxiii Part I. Preliminaries Chapter 1. Probab ility and Statistics 1 1.1 Probabilities and Events 1 1.2 Random Variabl es and Distributions 5 1.3 Random Number Generators 11 1.4 Moments 14 1.5 Convergence of Random Sequences 22 1.6 Basic Ideas About Stochastic Pr ocesses 26 1.7 Diffusion Processes 34 1.8 Wiener Processes and White Noi se 40 1.9 Statistical Tests and Estimation 44 Chapter 2. Probability and

57. CogNet: New Approximations Of Differential Entropy For Independent Component Ana New approximations of Differential Entropy for Independent Component Analysis and issomewhat similar to the classical polynomial density expansions by Gram http://cognet.mit.edu/posters/poster.tcl?publication_id=1983

58. PROBLEMS OF THE NUMERICAL ANALYSIS OF ITO STOCHASTIC DIFFERENTIAL Chapter 4 ends with a discussion of various expansions and approximations of multiplestochastic Stratonovich integrals on polynomial and trigonometric systems http://www.neva.ru/journal/eng/ref/1998/vol1/e_kulbk.htm

PROBLEMS OF THE NUMERICAL ANALYSIS OF ITO STOCHASTIC DIFFERENTIAL EQUATIONS The monograth D.F.Kuznetsov Department of Mathematics St.-Petersburg State Technical University St.-Petersburg, Russia, e-mail: control1@citadel.stu.neva.ru Abstract. The book is devoted to the problem of numerical analysis of Ito stochastic differential equations. The book consists of seven chapters. Chapter 1 is an introduction and begins with an exposition of general facts from the elementary theory of probability. Some problems formulated in terms of stochastic differential equations are presented. Chapter 2 deals with the problem of integration order replacement for multiple stochastic Ito integrals. For one class of multiple stochastic Ito integrals we give proofs of the integration order replacement theorems. Stochastic (Taylor-Ito, Taylor-Stratonovich, and unified Taylor-Ito) expansions of Ito processes are considered in Chapter 3. The unified Taylor-Ito expansions are constructed via integration order replacement theorems for multiple stochastic Ito integrals obtained in Chapter 2. Examples of the unified Taylor-Ito expansions for solutions of certain scalar and vector stochastic differential Ito equations are given. Chapter 4 provides methods of expansion and approximation of multiple stochastic Stratonovich and Ito's integrals. We give a new method of multiple Stratonovich stochastic integral approximation based on multiple Fourier series on full orthonormal systems of functions. The comparison of this method with the Milstein method of expansion and approximation of multiple stochastic Stratonovich integrals is given. General formulas for expansion, approximation, and mean-square error of approximation of multiple stochastic Stratonovich integral of a multiplicity k are obtained. We suggest a new method of multiple Ito stochastic integral approximation based on multiple integral sums. Chapter 4 ends with a discussion of various expansions and approximations of multiple stochastic Stratonovich integrals on polynomial and trigonometric systems of functions.

59. Abstract 99-3: Nonlinear Functionals Of Wavelet Expansions -- Adaptive Reconstru efficient evaluation of nonlinear expressions of wavelet expansions obtained through productsof wavelets with compositions to approximations of compositions http://www.zib.de/dfg-echtzeit/Publikationen/Preprints/Preprint-99-3.html

Preprint 99-3 Wolfgang Dahmen, Reinhold Schneider, Yuesheng Xu Nonlinear functionals of wavelet expansions Adaptive reconstruction and fast evaluation Keywords: Norm equivalences, nonlinear functions of multiscale expansions, adaptive schemes, best local polynomial approximation MSC: Abstract: E-mail of contact person : dahmen@igpm.rwth-aachen.de

60. Lai, T. L. And Wang, J. Q. Z. (1993). Edgeworth Expansions For Symmetric Statist addition, Edgeworth expansions are also developed for the bootstrap distributionsof these symmetric statistics, showing that the bootstrap approximations are http://www.stat.sinica.edu.tw/statistica/j3n2/j3n216/j3n216.htm

Statistica Sinica EDGEWORTH EXPANSIONS FOR SYMMETRIC STATISTICS WITH APPLICATIONS TO BOOTSTRAP METHODS Tze Leung Lai and Julia Qizhi Wang Stanford University and University of Minnesota Abstract: Edgeworth expansions are developed for a general class of symmetric statistics. Applications of the results are given to obtain approximations to the sampling distributions of statistics in the random censorship model and of linear combinations of order statistics. In addition, Edgeworth expansions are also developed for the bootstrap distributions of these symmetric statistics, showing that the bootstrap approximations are accurate to the order of O p n Key words and phrases: Efron-Stein ANOVA decomposition, asymptotic U -statis- tics, Edgeworth expansions, bootstrap, random censorship model, cumulative hazard function, log-rank statistics, linear combinations of order statistics.

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