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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/8874668 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 2314-4629 2314-4785 |