Abstract
Quasi-interpolation is very useful in the study of the approximation theory and its applications, since the method can yield solutions directly and does not require solving any linear system of equations. However, quasi-interpolation is usually discussed only for gridded data in the literature. In this paper we shall introduce a generalized Strang–Fix condition, which is related to nonstationary quasi-interpolation. Based on the discussion of the generalized Strang–Fix condition we shall generalize our quasi-interpolation scheme for multivariate scattered data, too.
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Communicated by Z. Wu and B.Y.C. Hon
AMS subject classification
41A63, 41A25, 65D10
Zong Min Wu: Supported by NSFC No. 19971017 and NOYG No. 10125102.
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Wu, Z.M., Liu, J.P. Generalized Strang–Fix condition for scattered data quasi-interpolation. Adv Comput Math 23, 201–214 (2005). https://doi.org/10.1007/s10444-004-1832-6
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DOI: https://doi.org/10.1007/s10444-004-1832-6