Advanced Algorithm for Interpolation with Wendland Functions

Hjortur Bjornsson; Sigurdur Hafstein

doi:10.1007/978-3-030-63193-2_6

Advanced Algorithm for Interpolation with Wendland Functions

Hjortur Bjornsson^*, Sigurdur Hafstein

^*Corresponding author for this work

Faculty of Physical Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Citation (Scopus)

Abstract

We develop and study algorithms for computing Lyapunov functions using meshless collocation and Wendland functions. We present a software tool that generates a C/C++ library that implements Wendland functions of arbitrary order in a specified factorized form with advantageous numerical properties. Additionally, we describe the algorithm used by the tool to generate these Wendland functions. Our factorized form is more efficient and has higher numerical accuracy than previous implementations. We develop and implement optimal grid generation for the interpolation problem using the Wendland functions. Finally, we present software that calculates Lyapunov functions using these Wendland functions and the optimally generated grid. The software tool and library are available for download with examples of usage.

Original language	English
Title of host publication	Informatics in Control, Automation and Robotics - 16th International Conference, ICINCO 2019, Revised Selected Papers
Editors	Oleg Gusikhin, Kurosh Madani, Janan Zaytoon
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	99-117
Number of pages	19
ISBN (Print)	9783030631925
DOIs	https://doi.org/10.1007/978-3-030-63193-2_6
Publication status	Published - 4 Dec 2020
Event	16th International Conference on Informatics in Control, Automation and Robotics, ICINCO 2019 - Prague, Czech Republic Duration: 29 Jul 2019 → 31 Jul 2019

Publication series

Name	Lecture Notes in Electrical Engineering
Volume	720
ISSN (Print)	1876-1100
ISSN (Electronic)	1876-1119

Conference

Conference	16th International Conference on Informatics in Control, Automation and Robotics, ICINCO 2019
Country/Territory	Czech Republic
City	Prague
Period	29/07/19 → 31/07/19

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Other keywords

Code generation
Lyapunov functions
Radial basis functions
Wendland function

Access to Document

10.1007/978-3-030-63193-2_6

Cite this

Bjornsson, H., & Hafstein, S. (2020). Advanced Algorithm for Interpolation with Wendland Functions. In O. Gusikhin, K. Madani, & J. Zaytoon (Eds.), Informatics in Control, Automation and Robotics - 16th International Conference, ICINCO 2019, Revised Selected Papers (pp. 99-117). (Lecture Notes in Electrical Engineering; Vol. 720). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-63193-2_6

Bjornsson, Hjortur ; Hafstein, Sigurdur. / Advanced Algorithm for Interpolation with Wendland Functions. Informatics in Control, Automation and Robotics - 16th International Conference, ICINCO 2019, Revised Selected Papers. editor / Oleg Gusikhin ; Kurosh Madani ; Janan Zaytoon. Springer Science and Business Media Deutschland GmbH, 2020. pp. 99-117 (Lecture Notes in Electrical Engineering).

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title = "Advanced Algorithm for Interpolation with Wendland Functions",

abstract = "We develop and study algorithms for computing Lyapunov functions using meshless collocation and Wendland functions. We present a software tool that generates a C/C++ library that implements Wendland functions of arbitrary order in a specified factorized form with advantageous numerical properties. Additionally, we describe the algorithm used by the tool to generate these Wendland functions. Our factorized form is more efficient and has higher numerical accuracy than previous implementations. We develop and implement optimal grid generation for the interpolation problem using the Wendland functions. Finally, we present software that calculates Lyapunov functions using these Wendland functions and the optimally generated grid. The software tool and library are available for download with examples of usage.",

keywords = "Code generation, Lyapunov functions, Radial basis functions, Wendland function",

author = "Hjortur Bjornsson and Sigurdur Hafstein",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.; 16th International Conference on Informatics in Control, Automation and Robotics, ICINCO 2019 ; Conference date: 29-07-2019 Through 31-07-2019",

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Bjornsson, H & Hafstein, S 2020, Advanced Algorithm for Interpolation with Wendland Functions. in O Gusikhin, K Madani & J Zaytoon (eds), Informatics in Control, Automation and Robotics - 16th International Conference, ICINCO 2019, Revised Selected Papers. Lecture Notes in Electrical Engineering, vol. 720, Springer Science and Business Media Deutschland GmbH, pp. 99-117, 16th International Conference on Informatics in Control, Automation and Robotics, ICINCO 2019, Prague, Czech Republic, 29/07/19. https://doi.org/10.1007/978-3-030-63193-2_6

Advanced Algorithm for Interpolation with Wendland Functions. / Bjornsson, Hjortur; Hafstein, Sigurdur.
Informatics in Control, Automation and Robotics - 16th International Conference, ICINCO 2019, Revised Selected Papers. ed. / Oleg Gusikhin; Kurosh Madani; Janan Zaytoon. Springer Science and Business Media Deutschland GmbH, 2020. p. 99-117 (Lecture Notes in Electrical Engineering; Vol. 720).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - We develop and study algorithms for computing Lyapunov functions using meshless collocation and Wendland functions. We present a software tool that generates a C/C++ library that implements Wendland functions of arbitrary order in a specified factorized form with advantageous numerical properties. Additionally, we describe the algorithm used by the tool to generate these Wendland functions. Our factorized form is more efficient and has higher numerical accuracy than previous implementations. We develop and implement optimal grid generation for the interpolation problem using the Wendland functions. Finally, we present software that calculates Lyapunov functions using these Wendland functions and the optimally generated grid. The software tool and library are available for download with examples of usage.

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KW - Radial basis functions

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Bjornsson H, Hafstein S. Advanced Algorithm for Interpolation with Wendland Functions. In Gusikhin O, Madani K, Zaytoon J, editors, Informatics in Control, Automation and Robotics - 16th International Conference, ICINCO 2019, Revised Selected Papers. Springer Science and Business Media Deutschland GmbH. 2020. p. 99-117. (Lecture Notes in Electrical Engineering). doi: 10.1007/978-3-030-63193-2_6

Advanced Algorithm for Interpolation with Wendland Functions

Abstract

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