NDLI: A new class of non-linear monotone Hermite interpolants

Content Provider	Springer Nature Link
Author	Yáñez, Dionisio F. Aràndiga, Francesc Baeza, Antonio
Copyright Year	2012
Abstract	Monotonicity-preserving approximation methods are used in numerous applications. These methods are expected to reconstruct a function from a discrete set of data preserving Monotonicity properties (i.e., the reconstructed function has to be monotone wherever the discrete data are). Most Monotonicity-preserving methods sacrifice accuracy in order to obtain Monotonicity. In this work we propose and analyze a Monotonicity-preserving Hermite interpolant that does not fully sacrifice accuracy. A key ingredient in the proposed technique is the approximation of derivatives using ENO (Essentially Non Oscillatory) and WENO (Weighted Essentially Non Oscillatory) interpolatory techniques. Then, an appropriate filtering process ensures the preservation of Monotonicity while maintaining, at the same time, the order of accuracy as high as possible. We perform several numerical experiments which confirm the properties of the proposed algorithms and compare them to other standard interpolatory approximation techniques.
Ending Page	309
Page Count	21
Starting Page	289
File Format	PDF
ISSN	10197168
e-ISSN	15729044
Journal	Advances in Computational Mathematics
Issue Number	2
Volume Number	39
Language	English
Publisher	Springer US
Publisher Date	2012-09-14
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Interpolation Hermite Algebra Approximation by polynomials Calculus of Variations and Optimal Control; Optimization Numeric Computing Non-linear Mathematics Theory of Computation Monotonicity
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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