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         Approximations Expansions:     more books (94)
  1. Asymptotology: Ideas, Methods, and Applications (Mathematics and Its Applications) by Igor V. Andrianov, Leonid I. Manevitch, 2002-11-30
  2. Multiscale Problems and Methods in Numerical Simulations: Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 9-15, 2001 ... Mathematics / Fondazione C.I.M.E., Firenze) by James H. Bramble, Albert Cohen, et all 2004-01-12
  3. Exponential Sums and their Applications (Mathematics and its Applications) by N.M Korobov, 2010-11-02
  4. Symbolic Asymptotics (Algorithms and Computation in Mathematics) by John R. Shackell, 2010-11-02
  5. Singular Integral Operators, Factorization and Applications: International Workshop on Operator Theory and Applications IWOTA 2000, Portugal (Operator Theory: Advances and Applications)
  6. Haar Series and Linear Operators (Mathematics and Its Applications) by I. Novikov, E. Semenov, 2010-11-02
  7. Nonsmooth Equations in Optimization: Regularity, Calculus, Methods and Applications (Nonconvex Optimization and Its Applications) by Diethard Klatte, B. Kummer, 2010-11-02
  8. Spline Functions and Multivariate Interpolations (Mathematics and Its Applications) by Borislav D. Bojanov, H. Hakopian, et all 2010-11-02
  9. Total Positivity and its Applications (Mathematics and Its Applications)
  10. The FitzHugh-Nagumo Model: Bifurcation and Dynamics (Mathematical Modelling: Theory and Applications) by C. Rocsoreanu, A. Georgescu, et all 2010-11-02
  11. Global Analysis in Linear Differential Equations (Mathematics and Its Applications) by M. Kohno, 1999-04-30
  12. The Theory of Cubature Formulas (Mathematics and Its Applications) by S.L. Sobolev, Vladimir L. Vaskevich, 2010-11-02
  13. Multivariate Spline Functions and Their Applications (Mathematics and Its Applications) by Ren-Hong Wang, 2010-11-02
  14. Functional Equations, Inequalities and Applications

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:

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

    GAMS (Generalized Algebraic Modeling System) Development Corporation

    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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