Sparse Grids and Applications

In the recent decade, there has been a growing interest in the numerical treatment of high-dimensional problems. It is well known that classical numerical discretization schemes fail in more than three or four dimensions due to the curse of dimensionality. The technique of sparse grids helps overcome this problem to some extent under suitable regularity assumptions. This discretization approach is obtained from a multi-scale basis by a tensor product construction and subsequent truncation of the resulting multiresolution series expansion. This volume of LNCSE is a collection of the papers from the proceedings of the workshop on sparse grids and its applications held in Bonn in May 2011. The selected articles present recent advances in the mathematical understanding and analysis of sparse grid discretization. Aspects arising from applications are given particular attention.

List of contents

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About the author

Dr. Michael Griebel ist Ordinarius für Wissenschaftliches Rechnen am Institut für Angewandte Mathematik der Universität in Bonn.

Summary

In the recent decade, there has been a growing interest in the numerical treatment of high-dimensional problems. It is well known that classical numerical discretization schemes fail in more than three or four dimensions due to the curse of dimensionality. The technique of sparse grids helps overcome this problem to some extent under suitable regularity assumptions. This discretization approach is obtained from a multi-scale basis by a tensor product construction and subsequent truncation of the resulting multiresolution series expansion. This volume of LNCSE is a collection of the papers from the proceedings of the workshop on sparse grids and its applications held in Bonn in May 2011. The selected articles present recent advances in the mathematical understanding and analysis of sparse grid discretization. Aspects arising from applications are given particular attention.

Product details

• Assisted by: Joche Garcke (Editor), Jochen Garcke (Editor), Griebel (Editor), Griebel (Editor), Michael Griebel (Editor)
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2014
• EAN: 9783642426605
• ISBN: 978-3-642-42660-5
• No. of pages: 286
• Dimensions: 155 mm x 16 mm x 235 mm
• Weight: 453 g
• Illustrations: X, 286 p.
• Series: Lecture Notes in Computational Science and Engineering; Lecture Notes in Computational Science and Engineering
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; C, Mathematics and Statistics, Mathematics of Computing, Computational Mathematics and Numerical Analysis, Computer mathematics, Mathematical theory of computation, Computational Science and Engineering, Maths for scientists, Computer science—Mathematics, Maths for computer scientists, adaptivity;high-dimensional approximation;sparse grids