<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In the present work, we analyze a technique designed by Geraci et al. in [<xref ref-type="bibr" rid="j_AMNS.2017.2.00030_ref_001_w2aab3b7b4b1b6b1ab1b7b1Aa">1</xref>,<xref ref-type="bibr" rid="j_AMNS.2017.2.00030_ref_011_w2aab3b7b4b1b6b1ab1b7c11Aa">11</xref>] named the Truncate and Encode (TE) strategy. It was presented as a non-intrusive method for steady and non-steady Partial Differential Equations (PDEs) in Uncertainty Quantification (UQ), and as a weakly intrusive method in the unsteady case.</p><p>We analyze the TE algorithm applied to the approximation of functions, and in particular its performance for piecewise smooth functions. We carry out some numerical experiments, comparing the performance of the algorithm when using different linear and non-linear interpolation techniques and provide some recommendations that we find useful in order to achieve a high performance of the algorithm.</p></abstract>

In the present work, we analyze a technique designed by Geraci et al. in [1,11] named the Truncate and Encode (TE) strategy. It was presented as a non-intrusive method for steady and non-steady Partial Differential Equations (PDEs) in Uncertainty Quantification (UQ), and as a weakly intrusive method in the unsteady case.We analyze the TE algorithm applied to the approximation of functions, and in particular its performance for piecewise smooth functions. We carry out some numerical experiments, comparing the performance of the algorithm when using different linear and non-linear interpolation techniques and provide some recommendations that we find useful in order to achieve a high performance of the algorithm.

High-accuracy approximation of piecewise smooth functions using the Truncation and Encode approach

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In the present work, we analyze a technique designed by Geraci et al. in [1,11] named the Truncate and Encode (TE) strategy. It was presented as a...

High-accuracy approximation of piecewise smooth functions using the Truncation and Encode approach

Published Online: Sep 06, 2017

Page range: 367 - 384

Received: Apr 07, 2017

Accepted: Sep 06, 2017

DOI: https://doi.org/10.21042/AMNS.2017.2.00030

Keywords
Truncate and Encode, Harten’s Multiresolution Framework, Approximation, Uncertainty Quantification, Piecewise smooth functions

© 2017 Rosa Donat, Sergio López-Ureña, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

High-accuracy approximation of piecewise smooth functions using the Truncation and Encode approach

Published Online: Sep 06, 2017

Page range: 367 - 384

Received: Apr 07, 2017

Accepted: Sep 06, 2017

DOI: https://doi.org/10.21042/AMNS.2017.2.00030

KeywordsTruncate and Encode, Harten’s Multiresolution Framework, Approximation, Uncertainty Quantification, Piecewise smooth functions

© 2017 Rosa Donat, Sergio López-Ureña, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Truncate and Encode, Harten’s Multiresolution Framework, Approximation, Uncertainty Quantification, Piecewise smooth functions