Sharp asymptotics of the Lp approximation error for interpolation on block partitions

Numerische Mathematik

Volumn 117, Issue 3, 2011, Pages 397-423

  Babenko, Yuliya ^a   Leskevich, Tatyana ^b   Mirebeau, Jean Marie ^c,d  

^a KENNESAW STATE UNIVERSITY   (United States)

^b OLES HONCHAR DNIPRO NATIONAL UNIVERSITY   (Ukraine)

^c UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^d CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79751526501     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-010-0355-y     Document Type: Article

References (12)

1. Babenko V. F.: Interpolation of continuous functions by piecewise linear ones. Math. Notes 24(1), 43-53 (1978).
2. 2 functions. East J. Approx. 12(1), 71-101 (2006).
3. p,Ω-error of linear spline interpolation. East J. Approx. 14(3), 285-317 (2008).
4. Babenko, Yu.: On the asymptotic behavior of the optimal error of spline interpolation of multivariate functions. PhD thesis (2006).
5. Babenko, Yu.: Exact asymptotics of the uniform error of interpolation by multilinear splines. J. Approx. Theory (to appear).
6. Böröczky K., Ludwig M.: Approximation of convex bodies and a momentum lemma for power diagrams. Monatsh. für Math. 127(2), 101-110 (1999).
7. Cohen, A., Mirebeau, J.-M.: Adaptive and Anisotropic Piecewise Polynomial Approximation, Chapter 4 of the Book Multiscale, Nonlinear and Adaptive Approximation. Springer, Berlin (2009).
8. D'Azevedo E. F.: Are bilinear quadrilaterals better than linear triangles?. SIAM J. Sci. Comput. 22(1), 198-217 (2000).
9. Fejes Toth, L.: Lagerungen in der Ebene, auf der Kugel und im Raum. 198-217 2nd edn. Springer, Berlin (1972).
10. d. Monatsh. Math. 135, 279-304 (2002).
11. Ligun, A. A., Shumeiko, A. A.: Asymptotic methods of curve recovery. Kiev. Inst. of Math. NAS of Ukraine, (in Russian) (1997).
12. Mirebeau J.-M.: Optimal meshes for finite elements of arbitrary order. Construct. Approx. 32(2), 339-383 (2010).