Abel–Goncharov Type Multiquadric Quasi-Interpolation Operators with Higher Approximation Order
A kind of Abel–Goncharov type operators is surveyed. The presented method is studied by combining the known multiquadric quasi-interpolant with univariate Abel–Goncharov interpolation polynomials. The construction of new quasi-interpolants ℒmAGf has the property of mm∈ℤ,m>0 degree polynomial repr...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/8874668 |
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| author | Ruifeng Wu |
| author_facet | Ruifeng Wu |
| author_sort | Ruifeng Wu |
| collection | DOAJ |
| description | A kind of Abel–Goncharov type operators is surveyed. The presented method is studied by combining the known multiquadric quasi-interpolant with univariate Abel–Goncharov interpolation polynomials. The construction of new quasi-interpolants ℒmAGf has the property of mm∈ℤ,m>0 degree polynomial reproducing and converges up to a rate of m+1. In this study, some error bounds and convergence rates of the combined operators are studied. Error estimates indicate that our operators could provide the desired precision by choosing the suitable shape-preserving parameter c and a nonnegative integer m. Several numerical comparisons are carried out to verify a higher degree of accuracy based on the obtained scheme. Furthermore, the advantage of our method is that the associated algorithm is very simple and easy to implement. |
| format | Article |
| id | doaj-art-b1a7d706c3b14eb49c03a518b4f11ba1 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-b1a7d706c3b14eb49c03a518b4f11ba12025-02-03T01:04:18ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/88746688874668Abel–Goncharov Type Multiquadric Quasi-Interpolation Operators with Higher Approximation OrderRuifeng Wu0School of Applied Mathematics, Jilin University of Finance and Economics, Changchun 130117, ChinaA kind of Abel–Goncharov type operators is surveyed. The presented method is studied by combining the known multiquadric quasi-interpolant with univariate Abel–Goncharov interpolation polynomials. The construction of new quasi-interpolants ℒmAGf has the property of mm∈ℤ,m>0 degree polynomial reproducing and converges up to a rate of m+1. In this study, some error bounds and convergence rates of the combined operators are studied. Error estimates indicate that our operators could provide the desired precision by choosing the suitable shape-preserving parameter c and a nonnegative integer m. Several numerical comparisons are carried out to verify a higher degree of accuracy based on the obtained scheme. Furthermore, the advantage of our method is that the associated algorithm is very simple and easy to implement.http://dx.doi.org/10.1155/2021/8874668 |
| spellingShingle | Ruifeng Wu Abel–Goncharov Type Multiquadric Quasi-Interpolation Operators with Higher Approximation Order Journal of Mathematics |
| title | Abel–Goncharov Type Multiquadric Quasi-Interpolation Operators with Higher Approximation Order |
| title_full | Abel–Goncharov Type Multiquadric Quasi-Interpolation Operators with Higher Approximation Order |
| title_fullStr | Abel–Goncharov Type Multiquadric Quasi-Interpolation Operators with Higher Approximation Order |
| title_full_unstemmed | Abel–Goncharov Type Multiquadric Quasi-Interpolation Operators with Higher Approximation Order |
| title_short | Abel–Goncharov Type Multiquadric Quasi-Interpolation Operators with Higher Approximation Order |
| title_sort | abel goncharov type multiquadric quasi interpolation operators with higher approximation order |
| url | http://dx.doi.org/10.1155/2021/8874668 |
| work_keys_str_mv | AT ruifengwu abelgoncharovtypemultiquadricquasiinterpolationoperatorswithhigherapproximationorder |