The harmonic polynomial method for solving the Cauchy problem connected with the Laplace equation.

This paper is concerned with the Cauchy problem connected with the Laplace equation. We investigate the denseness of harmonic polynomials and propose a numerical method for approximating the solution to the problem. The convergence and stability are analyzed with a suitable choice of the regularization method. Numerical experiments are also presented to show the effectiveness of our method. [ABSTRACT FROM AUTHOR]