Computing Highly Oscillatory Integrals
2018年1月 · Other Titles in Applied Mathematics 186 巻 · SIAM
4.0star
2 件のレビューreport
電子書籍
190
ページ
family_home
利用可能
info
report評価とレビューは確認済みではありません 詳細
この電子書籍について
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.
評価とレビュー
4.0
2 件のレビュー
この電子書籍を評価する
ご感想をお聞かせください。
読書情報
スマートフォンとタブレット
Android や iPad / iPhone 用の Google Play ブックス アプリをインストールしてください。このアプリがアカウントと自動的に同期するため、どこでもオンラインやオフラインで読むことができます。
ノートパソコンとデスクトップ パソコン
Google Play で購入したオーディブックは、パソコンのウェブブラウザで再生できます。
電子書籍リーダーなどのデバイス
Kobo 電子書籍リーダーなどの E Ink デバイスで読むには、ファイルをダウンロードしてデバイスに転送する必要があります。サポートされている電子書籍リーダーにファイルを転送する方法について詳しくは、ヘルプセンターをご覧ください。
