The best uniform quadratic approximation of circular arcs with high accuracy
In this article, the issue of the best uniform approximation of circular arcs with parametrically defined polynomial curves is considered. The best uniform approximation of degree 2 to a circular arc is given in explicit form. The approximation is constructed so that the error function is the Chebys...
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| Format: | Article |
| Language: | English |
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De Gruyter
2016-01-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2016-0012 |
| _version_ | 1818716519675199488 |
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| author | Rababah Abedallah |
| author_facet | Rababah Abedallah |
| author_sort | Rababah Abedallah |
| collection | DOAJ |
| description | In this article, the issue of the best uniform approximation of circular arcs with parametrically defined polynomial curves is considered. The best uniform approximation of degree 2 to a circular arc is given in explicit form. The approximation is constructed so that the error function is the Chebyshev polynomial of degree 4; the error function equioscillates five times; the approximation order is four. For θ = π/4 arcs (quarter of a circle), the uniform error is 5.5 × 10−3. The numerical examples demonstrate the efficiency and simplicity of the approximation method as well as satisfy the properties of the best uniform approximation and yield the highest possible accuracy. |
| first_indexed | 2024-12-17T19:20:33Z |
| format | Article |
| id | doaj.art-f9bd1bf33e754ad9b205ceefd7dabf1c |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-17T19:20:33Z |
| publishDate | 2016-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-f9bd1bf33e754ad9b205ceefd7dabf1c2022-12-21T21:35:35ZengDe GruyterOpen Mathematics2391-54552016-01-0114111812710.1515/math-2016-0012math-2016-0012The best uniform quadratic approximation of circular arcs with high accuracyRababah Abedallah0Abedallah Rababah: Department of Mathematics and Statistics, Jordan University of Science and Technology, 22110 Irbid, JordanIn this article, the issue of the best uniform approximation of circular arcs with parametrically defined polynomial curves is considered. The best uniform approximation of degree 2 to a circular arc is given in explicit form. The approximation is constructed so that the error function is the Chebyshev polynomial of degree 4; the error function equioscillates five times; the approximation order is four. For θ = π/4 arcs (quarter of a circle), the uniform error is 5.5 × 10−3. The numerical examples demonstrate the efficiency and simplicity of the approximation method as well as satisfy the properties of the best uniform approximation and yield the highest possible accuracy.https://doi.org/10.1515/math-2016-0012bézier curvesquadratic best uniform approximationcircular archigh accuracyapproximation orderequioscillation41a1041a2541a5065d1765d18 |
| spellingShingle | Rababah Abedallah The best uniform quadratic approximation of circular arcs with high accuracy Open Mathematics bézier curves quadratic best uniform approximation circular arc high accuracy approximation order equioscillation 41a10 41a25 41a50 65d17 65d18 |
| title | The best uniform quadratic approximation of circular arcs with high accuracy |
| title_full | The best uniform quadratic approximation of circular arcs with high accuracy |
| title_fullStr | The best uniform quadratic approximation of circular arcs with high accuracy |
| title_full_unstemmed | The best uniform quadratic approximation of circular arcs with high accuracy |
| title_short | The best uniform quadratic approximation of circular arcs with high accuracy |
| title_sort | best uniform quadratic approximation of circular arcs with high accuracy |
| topic | bézier curves quadratic best uniform approximation circular arc high accuracy approximation order equioscillation 41a10 41a25 41a50 65d17 65d18 |
| url | https://doi.org/10.1515/math-2016-0012 |
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