Buch, Englisch, 227 Seiten, Format (B × H): 162 mm x 242 mm, Gewicht: 476 g
ISBN: 978-0-8176-4170-2
Verlag: Birkhauser Boston
This book focuses primarily on a powerful tool: dimensionality reducing expansion (DRE). The method of DRE is a technique for changing a higher dimensional integration to a lower dimensional one with or without remainder. This work will appeal to a broad audience of students and researchers in pure and applied mathematics, statistics, and physics.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
- Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
- Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie
- Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
- Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
Weitere Infos & Material
1 Dimensionality Reducing Expansion of Multivariate Integration.- 1.1 Darboux formulas and their special forms.- 1.2 Generalized integration by parts rule.- 1.3 DREs with algebraic precision.- 1.4 Minimum estimation of remainders in DREs with algebraic precision.- 2 Boundary Type Quadrature Formulas with Algebraic Precision.- 2.1 Construction of BTQFs using DREs.- 2.2 BTQFs with homogeneous precision.- 2.3 Numerical integration associated with wavelet functions.- 2.4 Some applications of DREs and BTQFs.- 2.5 BTQFs over axially symmetric regions.- 3 The Integration and DREs of Rapidly Oscillating Functions.- 3.1 DREs for approximating a double integral.- 3.2 Basic lemma.- 3.3 DREs with large parameters.- 3.4 Basic expansion theorem for integrals with large parameters.- 3.5 Asymptotic expansion formulas for oscillatory integrals with singular factors.- 4 Numerical Quadrature Formulas Associated with the Integration of Rapidly Oscillating Functions.- 4.1 Numerical quadrature formulas of double integrals.- 4.2 Numerical integration of oscillatory integrals.- 4.3 Numerical quadrature of strongly oscillatory integrals with compound precision.- 4.4 Fast numerical computations of oscillatory integrals.- 4.5 DRE construction and numerical integration using measure theory.- 4.6 Error analysis of numerical integration.- 5 DREs Over Complex Domains.- 5.1 DREs of the double integrals of analytic functions.- 5.2 Construction of quadrature formulas using DREs.- 5.3 Integral regions suitable for DREs.- 5.4 Additional topics.- 6 Exact DREs Associated With Differential Equations.- 6.1 DREs and ordinary differential equations.- 6.2 DREs and partial differential equations.- 6.3 Applications of DREs in the construction of BTQFs.- 6.4 Applications of DREs in the boundary element method.
