Average-Case Analysis of Numerical Problems

2000
ISBN: 978-3-540-67449-8
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1733, 252 Seiten, Format (B × H): 155 mm x 233 mm, Gewicht: 408 g

Reihe: Lecture Notes in Mathematics

The average-case analysis of numerical problems is the counterpart of the more traditional worst-case approach. The analysis of average error and cost leads to new insight on numerical problems as well as to new algorithms. The book provides a survey of results that were mainly obtained during the last 10 years and also contains new results. The problems under consideration include approximation/optimal recovery and numerical integration of univariate and multivariate functions as well as zero-finding and global optimization. Background material, e.g. on reproducing kernel Hilbert spaces and random fields, is provided.

Zielgruppe

Research

Autoren/Hrsg.

Ritter, Klaus

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
• Mathematik | Informatik Mathematik Stochastik Elementare Stochastik

Inhaltsverzeichnis

Linear problems: Definitions and a classical example.- Second-order results for linear problems.- Integration and approximation of univariate functions.- Linear problems for univariate functions with noisy data.- Integration and approximation of multivariate functions.- Nonlinear methods for linear problems.- Nonlinear problems.