Quasi-interpolation has been a useful tool for data mining. In this talk, I shall introduce some recent developments of quasi-interpolation of our work team, including constructing kernels with higher-order generalized Strang-Fix conditions, meshless symplectic schemes for numerical solutions of partial differential equations based on quasi-interpolation, study and construction quasi-interpolation under the probabilistic numerical framework such as quasi-interpolation for irregularly spaced data, optimality and regularization properties of quasi-interpolation, and so on.
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