Computing Highly Oscillatory Integrals by Alfredo Deaño (4 results)
Language: English
Published by Society For Industrial & Applied Mathematics,U.S., 2018
- Softcover
Seller: Revaluation Books, Exeter, United KingdomRevaluation Books
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Language: English
Published by Society for Industrial and Applied Mathematics,U.S., US, 2018
- Softcover
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Paperback. Condition: New. 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 dema…nding. 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.
Language: English
Published by Society for Industrial & Applied Mathematics,U.S., 2017
- Softcover
Seller: THE SAINT BOOKSTORE, Southport, United KingdomTHE SAINT BOOKSTORE
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Language: English
Published by Society for Industrial and Applied Mathematics,U.S., US, 2018
- Softcover
Seller: Rarewaves.com UK, London, United KingdomRarewaves.com UK
Contact seller5-star sellerCondition: New
£ 74.64
£ 65.00 shippingShips from United Kingdom to U.S.A.Quantity: 1 available
Paperback. Condition: New. 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 dema…nding. 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.
