Bivariate High‐Accuracy Hermite‐Type Multiquadric Quasi‐Interpolation Operators

In this paper, a kind of Hermite‐type multiquadric quasi‐interpolation operator is constructed by combining an extended univariate multiquadric quasi‐interpolation operator with a bivariate Hermite interpolation polynomial. Some error bounds in terms of the modulus of continuity of high order and Peano representations for the error are given. Numerical comparisons with other existing methods are carried out to verify a higher degree of accuracy based on the obtained scheme. Furthermore, with an assumption on the suitable shape‐preserving parameter c , several numerical tests show that the convergent order of the proposed operator is satisfactory.