A Galerkin approximation method including space dimensional reduction - applied for solution of a heat conduction equation

A multivariate data fitting procedure, based on the Galerkin minimization method, is studied in this paper. The main idea of the developed approach consists in projecting the set of data points from the original, higher-dimensional space, onto a line section. Then, the approximation problem is solved in the resulting one-dimensional space. The elaborated recipe can be designed so that it is computationally more efficient than the schemes based on the least squares minimization. The performance of the method is studied by comparison with the least squares and the moving least squares procedures in a number of examples, including the solution of the heat diffusion equation.