Computing Highly Oscillatory Integrals
јан 2018. · Other Titles in Applied Mathematics 186. књига · SIAM
4,0star
2 recenzijereport
E-knjiga
190
Stranica
family_home
Ispunjava uslove
info
reportOcene i recenzije nisu verifikovane Saznajte više
O ovoj e-knjizi
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.
The text is intended for advanced undergraduate and graduate students, as well as applied mathematicians, scientists, and engineers who encounter highly oscillatory integrals as a critical difficulty in their computations.
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.
The text is intended for advanced undergraduate and graduate students, as well as applied mathematicians, scientists, and engineers who encounter highly oscillatory integrals as a critical difficulty in their computations.
Ocene i recenzije
4,0
2 recenzije
Ocenite ovu e-knjigu
Javite nam svoje mišljenje.
Informacije o čitanju
Pametni telefoni i tableti
Instalirajte aplikaciju Google Play knjige za Android i iPad/iPhone. Automatski se sinhronizuje sa nalogom i omogućava vam da čitate onlajn i oflajn gde god da se nalazite.
Laptopovi i računari
Možete da slušate audio-knjige kupljene na Google Play-u pomoću veb-pregledača na računaru.
E-čitači i drugi uređaji
Da biste čitali na uređajima koje koriste e-mastilo, kao što su Kobo e-čitači, treba da preuzmete fajl i prenesete ga na uređaj. Pratite detaljna uputstva iz centra za pomoć da biste preneli fajlove u podržane e-čitače.
