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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2025-06-01
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| author | David Levin Nira Gruberger |
| author_facet | David Levin Nira Gruberger |
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| description | 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. |
| format | Article |
| id | doaj-art-af4e992654674e1ba99166b7a801ed1f |
| institution | Kabale University |
| issn | 1999-4893 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
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| series | Algorithms |
| spelling | doaj-art-af4e992654674e1ba99166b7a801ed1f2025-08-20T03:30:29ZengMDPI AGAlgorithms1999-48932025-06-0118633510.3390/a18060335Adapted B-Spline Quasi-Interpolation for Approximating Piecewise Smooth FunctionsDavid Levin0Nira Gruberger1School of Mathematical Sciences, Tel-Aviv University, Tel Aviv 6997801, IsraelHolon Institue of Technology, Holon 5810201, IsraelWe 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.https://www.mdpi.com/1999-4893/18/6/335splinesquasi-interpolationpiecewise smooth functionsbivariate approximation |
| spellingShingle | David Levin Nira Gruberger Adapted B-Spline Quasi-Interpolation for Approximating Piecewise Smooth Functions Algorithms splines quasi-interpolation piecewise smooth functions bivariate approximation |
| title | Adapted B-Spline Quasi-Interpolation for Approximating Piecewise Smooth Functions |
| title_full | Adapted B-Spline Quasi-Interpolation for Approximating Piecewise Smooth Functions |
| title_fullStr | Adapted B-Spline Quasi-Interpolation for Approximating Piecewise Smooth Functions |
| title_full_unstemmed | Adapted B-Spline Quasi-Interpolation for Approximating Piecewise Smooth Functions |
| title_short | Adapted B-Spline Quasi-Interpolation for Approximating Piecewise Smooth Functions |
| title_sort | adapted b spline quasi interpolation for approximating piecewise smooth functions |
| topic | splines quasi-interpolation piecewise smooth functions bivariate approximation |
| url | https://www.mdpi.com/1999-4893/18/6/335 |
| work_keys_str_mv | AT davidlevin adaptedbsplinequasiinterpolationforapproximatingpiecewisesmoothfunctions AT niragruberger adaptedbsplinequasiinterpolationforapproximatingpiecewisesmoothfunctions |