MQ Quasi-Interpolation Operators: Adaptive Construction and Rigorous Approximation Bound Estimations

This paper focuses on constructing four novel multiquadric (MQ) quasi-interpolation operators. We conduct a comprehensive analysis of the essential properties of the proposed operators and further derive rigorous optimal upper and lower bounds for the approximation error. Numerical experiments are performed to verify the theoretical results, and the numerical outcomes are in excellent agreement with our theoretical analysis.