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In this paper, we present a new kind of quadratic approximation operator reproducing of both algebraic and trigonometric functions. It is called integro quadratic splines interpolant, which agree with the given integral values of a univariate real-valued function over the same intervals, rather than the functional values at the knots. Efficient approximations of fractional integrals and fractional Caputo derivatives based on this interpolant, are constructed and well studied. The general approximation error is studied too, and the super convergence property is also derived when the interval is equally partitioned. Numerical examples illustrate that our method is very effective and our quadratic algebraic trigonometric integro spline has higher approximation ability than others. K E Y W O R D Salgebraic trigonometric splines, error bound, fractional caputo derivatives, fractional integrals, integro spline quasi-interpolant

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A nonstandard low-cost spline approximation method for approximating bivariate functions is constructed. It is applied for Digital Elevation approximation and then its accuracy in the downscaling process is studied.