Abstract
We introduce a type of modified truncations of approximate approximation with Gaussian kernels, which can be applied to approximate functions on compact intervals. Our results improve the related results of Chen and Cao (Appl Math Comput 217:725---734, 2010), Muller and Varnhorn (J Approx Theory 145:171---181, 2007). Also, we construct approximate approximation operators in multivariate cases and obtain the estimates of approximation rate.
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