Adapted B-Spline Quasi-Interpolation for Approximating Piecewise Smooth Functions
We address the challenge of efficiently approximating piecewise smooth functions, particularly those with jump discontinuities. Given function values on a uniform grid over a domain <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-06-01
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| Series: | Algorithms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1999-4893/18/6/335 |
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| Summary: | We address the challenge of efficiently approximating piecewise smooth functions, particularly those with jump discontinuities. Given function values on a uniform grid over a domain <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Ω</mo></semantics></math></inline-formula> in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mi>d</mi></msup></semantics></math></inline-formula>, we present a novel B-spline-based approximation framework, using new adaptable quasi-interpolation operators. This approach integrates discontinuity detection techniques, allowing the quasi-interpolation operator to selectively use points from only one side of a discontinuity in both one- and two-dimensional cases. Among a range of candidate operators, the most suitable quasi-interpolation scheme is chosen to ensure high approximation accuracy and efficiency, while effectively suppressing spurious oscillations in the vicinity of discontinuities. |
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| ISSN: | 1999-4893 |