Numerical Differentiation for the Second Order Derivative of Functions with Several Variables

Abstract. We propose a regularized optimization problem for computing numerical differentiation for the second order derivative for functions with two variables from the noisy values of the function at scattered points, and give the proof of the existence and uniqueness of the solution of this problem. The reconstruction scheme is also given during the proof, which is based on biharmonic Green function. The convergence estimate of the regularized solution to the exact solution for the regularized optimization problem as the regularized parameter and discrepancy of noisy data tending to zero is provided under a simple choice of regularization parameter. In the end we give the numerical examples and analyze the computational results.