Abstract
A major shortcoming of the method of least squares, for the solution of partial differential equations, is the arbitrariness in the choice of the approximating functions. This shortcoming is eliminated by formulating the method of least squares as a variational principle and then by utilizing the iterative scheme used in the extended Kantorovich method to generate the approximating functions. The procedure is demonstrated on an example using a one term approximation. It is found that the obtained approximation agrees very closely with the exact solution, that the convergence of the iterative process is very rapid, and that the final form of the generated solution does not depend upon the initial choice.
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