03825nam 2200577 i 45000010014000000030005000140050017000190060019000360070015000550080041000700100017001110200030001280200025001580280016001830350025001990350022002240400040002460500023002860820016003091000044003252450099003692640150004683000026006183360021006443370026006653380032006914900047007235040051007705050332008215060072011535201376012255300037026015380036026385380047026745880054027216500015027756500024027906500024028146530021028386530015028596530024028746530021028986530027029196550022029467000030029687000026029987100064030247760053030888300041031418560065031829781611975123SIAM20171207190106.0m o d cr |||||||||||171129s2017 pau ob 001 0 eng d a 2017056799 a9781611975123qelectronic z9781611975116qprint51aOT155bSIAM a(CaBNVSL)thg00975247 a(OCoLC)1013497641 aCaBNVSLbengerdacCaBNVSLdCaBNVSL 4aQA308b.D43 2017eb04a515/.432231 aDea{tilde}no Gamallo, Alfredo,eauthor.10aComputing highly oscillatory integrals /cAlfredo Dea{tilde}no, Daan Huybrechs, Arieh Iserles. 1aPhiladelphia, Pennsylvania :bSociety for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104),c[2017] a1 PDF (x, 180 pages). atext2rdacontent aelectronic2isbdmedia aonline resource2rdacarrier1 aOther titles in applied mathematics ;v155 aIncludes bibliographical references and index.0 a1. Introduction -- 2. Asymptotic theory of highly oscillatory integrals -- 3. Filon and Levin methods -- 4. Extended Filon method -- 5. Numerical steepest descent -- 6. Complex-valued Gaussian quadrature -- 7. A highly oscillatory olympics -- 8. Variations on the highly oscillatory theme -- Appendix A. Orthogonal polynomials. aRestricted to subscribers or individual electronic text purchasers.3 aHighly oscillatory phenomena range across numerous areas in science and engineering and their computation represents a difficult challenge. A case in point is integrals of rapidly oscillating functions in one or more variables. The quadrature of such integrals has been historically considered very demanding. Research in the past 15 years (in which the authors played a major role) resulted in a range of very effective and affordable algorithms for highly oscillatory quadrature. This is the only monograph bringing together the new body of ideas in this area in its entirety. The starting point is that approximations need to be analyzed using asymptotic methods rather than by more standard polynomial expansions. As often happens in computational mathematics, once a phenomenon is understood from a mathematical standpoint, effective algorithms follow. As reviewed in this monograph, we now have at our disposal a number of very effective quadrature methods for highly oscillatory integrals--Filon-type and Levin-type methods, methods based on steepest descent, and complex-valued Gaussian quadrature. Their understanding calls for a fairly varied mathematical toolbox--from classical numerical analysis, approximation theory, and theory of orthogonal polynomials all the way to asymptotic analysis--yet this understanding is the cornerstone of efficient algorithms. aAlso available in print version. aMode of access: World Wide Web. aSystem requirements: Adobe Acrobat Reader. aDescription based on title page of print version. 0aIntegrals. 0aCalculus, Integral. 0aBifurcation theory. aHigh oscillation aQuadrature aAsymptotic analysis aSteepest descent aOrthogonal polynomials 0aElectronic books.1 aHuybrechs, Daan,eauthor.1 aIserles, A.,eauthor.2 aSociety for Industrial and Applied Mathematics,epublisher.08iPrint version:w(DLC) 2017042104z9781611975116 0aOther titles in applied mathematics.403SIAMuhttp://epubs.siam.org/doi/book/10.1137/1.9781611975123