Quasi-Interpolation Operators for Bivariate Quintic Spline Spaces and Their Applications
Abstract
:1. Introduction
2. The Bivariate Spline Space
2.1. The Spaces
2.2. Basis of
2.3. Quasi-Interpolation Operators for
3. Applications of Quasi-Interpolation Operator
3.1. Solving 2D Burgers’ Equations
3.2. Image Reconstruction
4. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Mesh Grid | ||||||
---|---|---|---|---|---|---|
(0.1, 0.1) | 0.61749 | 0.61720 | 0.59474 | 0.59439 | 0.55564 | 0.55568 |
(0.9, 0.2) | 0.50021 | 0.50020 | 0.50015 | 0.50014 | 0.50006 | 0.50007 |
(0.8, 0.3) | 0.50150 | 0.50148 | 0.50108 | 0.50102 | 0.50049 | 0.50048 |
(0.9, 0.5) | 0.50403 | 0.50398 | 0.50289 | 0.50275 | 0.50155 | 0.50130 |
(0.8, 0.6) | 0.52640 | 0.52667 | 0.51859 | 0.51896 | 0.50990 | 0.50933 |
(0.2, 0.8) | 0.74931 | 0.74930 | 0.74900 | 0.74898 | 0.74783 | 0.74786 |
(0.9, 0.9) | 0.61720 | 0.61720 | 0.59456 | 0.59439 | 0.55369 | 0.55568 |
Mesh Grid | ||||||
---|---|---|---|---|---|---|
(0.1, 0.1) | 0.88251 | 0.88280 | 0.90526 | 0.90561 | 0.94436 | 0.94432 |
(0.9, 0.2) | 0.99979 | 0.99980 | 0.99985 | 0.99986 | 0.99994 | 0.99993 |
(0.8, 0.3) | 0.99850 | 0.99852 | 0.99892 | 0.99898 | 0.99951 | 0.99952 |
(0.9, 0.5) | 0.99597 | 0.99602 | 0.99711 | 0.99725 | 0.99845 | 0.99869 |
(0.8, 0.6) | 0.97360 | 0.97333 | 0.98141 | 0.98104 | 0.99010 | 0.99067 |
(0.2, 0.8) | 0.75069 | 0.75070 | 0.75100 | 0.75102 | 0.75217 | 0.75214 |
(0.9, 0.9) | 0.88250 | 0.88280 | 0.90544 | 0.90561 | 0.94632 | 0.94432 |
Mesh Grid | ||||||
---|---|---|---|---|---|---|
MSQI | Bahadir [32] | Zhu [16] | MSQI | Bahadir [32] | Zhu [16] | |
(0.1, 0.1) | 1.63803 | 7.24132 | 5.91368 | 6.11973 | 5.13431 | 2.77664 |
(0.5, 0.1) | 1.85815 | 2.42869 | 4.84030 | 1.73489 | 8.85712 | 4.52081 |
(0.9, 0.1) | 1.64831 | 8.39751 | 3.41000 | 3.07314 | 6.53372 | 3.37430 |
(0.3, 0.3) | 1.65880 | 8.25331 | 5.91368 | 6.69829 | 7.31601 | 2.77664 |
(0.7, 0.3) | 1.94033 | 3.43163 | 4.84030 | 2.16464 | 6.27245 | 4.52081 |
(0.1, 0.5) | 1.61309 | 5.62014 | 1.64290 | 3.32546 | 4.01942 | 2.86553 |
Mesh Grid | ||||||
---|---|---|---|---|---|---|
MSQI | Bahadir [32] | Zhu [16] | MSQI | Bahadir [32] | Zhu [16] | |
(0.1, 0.1) | 1.63803 | 8.35601 | 5.91368 | 6.11973 | 6.17325 | 2.77664 |
(0.5, 0.1) | 1.85815 | 5.13642 | 4.84030 | 1.73489 | 4.67046 | 4.52081 |
(0.9, 0.1) | 1.64832 | 7.03298 | 3.41000 | 3.07314 | 1.70434 | 3.37400 |
(0.3, 0.3) | 1.65880 | 6.15201 | 5.91368 | 6.69829 | 6.25402 | 2.77664 |
(0.7, 0.3) | 1.94033 | 5.41000 | 4.84030 | 2.16464 | 4.66046 | 4.52081 |
(0.1, 0.5) | 1.61310 | 7.35192 | 1.64290 | 3.32546 | 8.72422 | 2.86553 |
Mesh Grid | [16] | [16] | ||||
---|---|---|---|---|---|---|
(0.1, 0.1) | 0.18367 | 3.29366 | 3.30750 | -0.02041 | 7.46922 | 1.05384 |
(0.3, 0.1) | 0.34693 | 5.45525 | 5.56160 | 0.18367 | 3.14176 | 3.30770 |
(0.2, 0.2) | 0.36734 | 6.41938 | 6.61520 | −0.04081 | 1.80110 | 2.10766 |
(0.4, 0.2) | 0.53060 | 8.79085 | 8.86940 | 0.16326 | 2.16219 | 2.25400 |
(0.3, 0.3) | 0.55101 | 9.85992 | 9.92330 | −0.06122 | 3.08212 | 3.16150 |
(0.2, 0.4) | 0.57142 | 1.00279 | 1.09769 | −0.28571 | 7.37580 | 8.57700 |
(0.5, 0.5) | 0.91835 | 1.65391 | 1.65386 | −0.10204 | 5.26189 | 5.26920 |
Mesh Grid | [16] | [16] | ||||
---|---|---|---|---|---|---|
(0.1, 0.1) | 0.17645 | 1.56636 | 1.01945 | −0.11762 | 2.30003 | 3.54833 |
(0.3, 0.1) | 0.23529 | 4.91795 | 5.58724 | 0.17646 | 1.53797 | 1.01946 |
(0.2, 0.2) | 0.35291 | 3.32840 | 2.03891 | −0.23524 | 5.73342 | 7.09666 |
(0.4, 0.2) | 0.41174 | 2.52872 | 6.60670 | 0.05884 | 1.73085 | 4.56779 |
(0.3, 0.3) | 0.52936 | 5.66418 | 3.05837 | −0.35284 | 1.04665 | 1.06450 |
(0.2, 0.4) | 0.64701 | 5.11863 | 4.89963 | −0.76460 | 1.07043 | 1.67222 |
(0.5, 0.5) | 0.88225 | 1.03951 | 5.09728 | −0.58804 | 1.92169 | 1.77417 |
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Yu, R.; Zhu, C.; Hou, X.; Yin, L. Quasi-Interpolation Operators for Bivariate Quintic Spline Spaces and Their Applications. Math. Comput. Appl. 2017, 22, 10. https://doi.org/10.3390/mca22010010
Yu R, Zhu C, Hou X, Yin L. Quasi-Interpolation Operators for Bivariate Quintic Spline Spaces and Their Applications. Mathematical and Computational Applications. 2017; 22(1):10. https://doi.org/10.3390/mca22010010
Chicago/Turabian StyleYu, Rengui, Chungang Zhu, Xianmin Hou, and Li Yin. 2017. "Quasi-Interpolation Operators for Bivariate Quintic Spline Spaces and Their Applications" Mathematical and Computational Applications 22, no. 1: 10. https://doi.org/10.3390/mca22010010
APA StyleYu, R., Zhu, C., Hou, X., & Yin, L. (2017). Quasi-Interpolation Operators for Bivariate Quintic Spline Spaces and Their Applications. Mathematical and Computational Applications, 22(1), 10. https://doi.org/10.3390/mca22010010