Algorithms for the construction of high-order Kronrod rule extensions with application to sparse-grid integration
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Date
2017-11
Publication Type
Journal Article
ETH Bibliography
yes
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Abstract
Gauss quadrature points are not nested so search for quadrature rules with nested points and similar efficiency are important. A well-studied source of candidates are the Kronrod-Patterson extensions. Under suitable conditions, it is possible to build towers of nested rules. We investigate this topic further and give a detailed description of the algorithms used for constructing such iterative extensions. Our new implementation combines several important ideas spread out in theoretical research papers. We apply the resulting algorithms to the classical orthogonal polynomials and build sparse high-dimensional quadrature rules for each class.
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published
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Journal / series
Volume
76 (3)
Pages / Article No.
617 - 637
Publisher
Springer
Event
Edition / version
Methods
Software
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Date collected
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Subject
Kronrod rule; Patterson extension; Nested quadrature; Smolyak construction; Genz-Keister rule; Sparse quadrature; High-dimensional quadrature; Orthogonal polynomial; Stieltjes polynomial
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Notes
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.
Funding
140688 - Numerical Semiclassical Quantum Dynamics with Wavepackets (SNF)