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Algorithm 1020: Computation of Multi-Degree Tchebycheffian B-Splines

Author:

Hendrik SpeleersAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 48, Issue 1

Article No.: 12, Pages 1 - 31

https://doi.org/10.1145/3478686

Published: 16 February 2022 Publication History

Abstract

Multi-degree Tchebycheffian splines are splines with pieces drawn from extended (complete) Tchebycheff spaces, which may differ from interval to interval, and possibly of different dimensions. These are a natural extension of multi-degree polynomial splines. Under quite mild assumptions, they can be represented in terms of a so-called multi-degree Tchebycheffian B-spline (MDTB-spline) basis; such basis possesses all the characterizing properties of the classical polynomial B-spline basis. We present a practical framework to compute MDTB-splines, and provide an object-oriented implementation in Matlab. The implementation supports the construction, differentiation, and visualization of MDTB-splines whose pieces belong to Tchebycheff spaces that are null-spaces of constant-coefficient linear differential operators. The construction relies on an extraction operator that maps local Tchebycheffian Bernstein functions to the MDTB-spline basis of interest.

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Cited By

Boushabi MEddargani SIbáñez MLamnii A(2024)Normalized B-spline-like representation for low-degree Hermite osculatory interpolation problemsMathematics and Computers in Simulation10.1016/j.matcom.2024.05.011225(98-110)Online publication date: Nov-2024
https://doi.org/10.1016/j.matcom.2024.05.011
Raval KManni CSpeleers H(2024)Adaptive isogeometric analysis based on locally refined Tchebycheffian B-splinesComputer Methods in Applied Mechanics and Engineering10.1016/j.cma.2024.117186430(117186)Online publication date: Oct-2024
https://doi.org/10.1016/j.cma.2024.117186
Bosner T(2024)High order approximation by CCC-spline quasi-interpolantsJournal of Computational and Applied Mathematics10.1016/j.cam.2023.115715442:COnline publication date: 17-Apr-2024
https://dl.acm.org/doi/10.1016/j.cam.2023.115715
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Index Terms

Algorithm 1020: Computation of Multi-Degree Tchebycheffian B-Splines
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
    2. Numerical analysis
      1. Interpolation

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Information

Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 48, Issue 1

March 2022

320 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/3505199

Editors:
Zhaojun Bai
University of California at Davis, USA
,
Wolfgang Bangerth
Colorado State University, USA

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 16 February 2022

Accepted: 01 July 2021

Revised: 01 June 2021

Received: 01 June 2020

Published in TOMS Volume 48, Issue 1

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Beyond Borders Programme of the University of Rome Tor Vergata through the project ASTRID
MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome Tor Vergata

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Cited By

Boushabi MEddargani SIbáñez MLamnii A(2024)Normalized B-spline-like representation for low-degree Hermite osculatory interpolation problemsMathematics and Computers in Simulation10.1016/j.matcom.2024.05.011225(98-110)Online publication date: Nov-2024
https://doi.org/10.1016/j.matcom.2024.05.011
Raval KManni CSpeleers H(2024)Adaptive isogeometric analysis based on locally refined Tchebycheffian B-splinesComputer Methods in Applied Mechanics and Engineering10.1016/j.cma.2024.117186430(117186)Online publication date: Oct-2024
https://doi.org/10.1016/j.cma.2024.117186
Bosner T(2024)High order approximation by CCC-spline quasi-interpolantsJournal of Computational and Applied Mathematics10.1016/j.cam.2023.115715442:COnline publication date: 17-Apr-2024
https://dl.acm.org/doi/10.1016/j.cam.2023.115715
Floater M(2024)On the positivity of B-spline WronskiansCalcolo10.1007/s10092-024-00613-061:3Online publication date: 10-Sep-2024
https://doi.org/10.1007/s10092-024-00613-0
Cho D(2023)Isogeometric Schwarz Preconditioners with Generalized B-Splines for the Biharmonic ProblemAxioms10.3390/axioms1205045212:5(452)Online publication date: 4-May-2023
https://doi.org/10.3390/axioms12050452
Raval KManni CSpeleers H(2023)Tchebycheffian B-splines in isogeometric Galerkin methodsComputer Methods in Applied Mechanics and Engineering10.1016/j.cma.2022.115648403(115648)Online publication date: Jan-2023
https://doi.org/10.1016/j.cma.2022.115648
Campagna RConti CCuomo S(2023)A linear algebra approach to HP-splines frequency parameter selectionApplied Mathematics and Computation10.1016/j.amc.2023.128241458:COnline publication date: 1-Dec-2023
https://dl.acm.org/doi/10.1016/j.amc.2023.128241
Eddargani SOraiche MLamnii ALouzar M(2022)C2 Cubic Algebraic Hyperbolic Spline Interpolating Scheme by Means of Integral ValuesMathematics10.3390/math1009149010:9(1490)Online publication date: 29-Apr-2022
https://doi.org/10.3390/math10091490

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