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Computing Highly Oscillatory Integrals
Af: Daan Huybrechs, Alfredo Deano, Arieh Iserles Engelsk Paperback
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Computing Highly Oscillatory Integrals
Af: Daan Huybrechs, Alfredo Deano, Arieh Iserles Engelsk Paperback
Highly 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.
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Highly 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.
Produktdetaljer
Sprog: Engelsk
Sider: 182
ISBN-13: 9781611975116
Indbinding: Paperback
Udgave:
ISBN-10: 1611975115
Kategori: Anvendt matematik
Udg. Dato: 30 jan 2018
Længde: 19mm
Bredde: 181mm
Højde: 261mm
Oplagsdato: 30 jan 2018
Forfatter(e) Daan Huybrechs, Alfredo Deano, Arieh Iserles


Kategori Anvendt matematik


Sprog Engelsk


Indbinding Paperback


Sider 182


Udgave


Længde 19mm


Bredde 181mm


Højde 261mm


Udg. Dato 30 jan 2018


Oplagsdato 30 jan 2018

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