Locally supported rational spline wavelets on a sphere

Mathematics of Computation

Volumn 74, Issue 252, 2005, Pages 1803-1829

  Roşca, Daniela ^a,b  

^a UNIVERSITY OF LÜBECK   (Germany)

^b TECHNICAL UNIVERSITY OF CLUJ NAPOCA   (Romania)

Author keywords

Interpolation; Multivariate approximation; Wavelets

Indexed keywords

EID: 27144542970     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-05-01754-0     Document Type: Article

References (24)

1. G. P. Bonneau, Optimal Triangular Haar Bases for Spherical Data, in IEEE Visualization '99, San Francisco, CA, 1999.
2. A. Cohen, L. M. Echeverry and Q. Sun, Finite Elements Wavelets, Report, University Pierre et Marie Curie, Paris, 2000.
3. 3, Numer. Funct. Anal. Optim. 16 (1995), 19-41. MR1322896 (96a:42044)
4. M. Floater and E. Quak, Piecewise Linear Prewavelets on Arbitrary Triangulations, Numer. Math. 82 (1999), 221-252. MR1685460 (2000a:42053)
5. M. Floater and E. Quak, A Semi-prewavelet Approach to Piecewise Linear Prewavelets on Triangulation, Approximation Theory IX (C.K. Chui and L.L. Schumaker, eds.), vol. 2, Vanderbilt University Press, 1998, pp. 63-70. MR1743034
6. M. Floater and E. Quak, Linear Independence and Stability of Piecewise Linear Prewavelets on Arbitrary Triangulations, SIAM J. Numer. Anal. 38 2000, no. 1, 58-79. MR1770342 (2001e:65237)
7. M. Floater, E. Quak and M. Reimers, Filter Bank Algorithms for Piecewise Linear Prewavelets on Arbitrary Triangulation, J. Comp. Appl. Math. 119 (2000), 185-207. MR1774217 (2001i:65145)
8. W. Freeden and U. Windheuser, Combined Spherical Harmonics and Wavelet Expansions -A Future Concept in Earth's Gravitational Potential Determination, Appl. Comput. Harm. Anal. 4 (1997), 1-37. MR1429676 (97j:86004)
9. J. Göttelmann, Locally Supported Wavelets on Manifolds with Applications to the 2D Sphere, Appl. Comput. Harm. Anal. 7 (1999), 1-33. MR1699606 (2000j:42051)
10. M. Lounsbery, T. DeRose and J. Warren, Multiresolution Analysis for Surfaces of Arbitrary Topological Type, ACM Transactions on Graphics 16 (1997), no. 1, 34-73.
11. F. Narcowich and J. D. Ward, Wavelets Associated with Periodic Basis Functions, Appl. Comput. Harm. Anal. 3 (1996), 40-56. MR1374394 (96j:42022)
12. F. Narcowich and J. D. Ward, Nonstationary Wavelets on the m-Sphere for scattered Data, Appl. Comput. Harm. Anal. 3 (1996), 324-336. MR1420501 (97h:42020)
13. G. Nielson, I. Jung and J. Sung, Haar Wavelets over Triangular Domains with Applications to Multiresolution Models for Flow over a Sphere, IEEE Visualization '97, IEEE 1997, pp. 143-150.
14. P. Oswald, Multilevel Finite Element Approximation: Theory and Applications, B. G. Teubner, Stuttgart, 1994. MR1312165 (95k:65110)
15. D. Potts and M. Tasche, Interpolatory Wavelets on the Sphere, Approximation Theory VIII (C. K. Chui and L. L. Schumaker, eds.), vol. 2, World Scientific, Singapore, 1995, pp. 335-342. MR1471800 (98e:42040)
16. D. Potts, G. Steidl and M. Tasche, Kernels of Spherical Harmonics and Spherical Frames, Advanced Topics in Multivariate Approximations (F. Fontanella, K. Jetter, P-J. Laurent, eds.), World Scientific, Singapore, 1996. MR1661417 (99g:42042)
17. D. Roşca, Haar wavelets on spherical triangulations, in Advances in Multiresolution for Geometric Modelling (N. A. Dodgson, M. S. Floater, M. A. Sabin, eds.), Springer Verlag, 2005, pp. 405-417.
18. D. Roşca, Optimal Haar wavelets on spherical triangulations, Pure Mathematics and Applications, Budapest (to appear).
19. D. Roşca, Piecewise Constant Wavelets Defined on Closed Surfaces, J. Comput. Anal. Appl. (to appear).
20. H. Schaeben, D. Potts and J. Prestin, Spherical Wavelets with Application in Preferred Crystallographic Orientation, IAMG' 2001, Cancun, 2001.
21. P. Schröder and W. Sweldens, Spherical Wavelets: Efficiently Representing Functions on the Sphere, Computer Graphics Proceedings (SIGGRAPH 95), 1995, pp. 161-172.
22. P. Schröder and W. Sweldens, Spherical Wavelets: Texture Processing, preprint.
23. L. Schumaker and C. Traas, Fitting Scattered Data on Sphere-like Surface Using Tensor Products of Trigonometric and Polynomial Splines, Numer. Math. 60 (1991), 133-144. MR1131503 (92j:65012)
24. 1-Wavelets on the Two-Dimensional Sphere, Appl. Comput. Harm. Anal. 10 (2001), 1-26. MR1808197 (2001k:42048)