The numerical solution of first kind integral equations (Q582854)

\textit{E. Babolian} and the second author [J. Inst. Math. Appl. 24, 157-174 (1979; Zbl 0428.65065)] developed a method for solving Fredholm integral equations of the first kind by expanding the solution as a finite Chebyshev series and imposing regularization constraints directly on the coefficients of the expansion. This involves the choice of two regularization parameters. In the current paper, G. Wahba's cross validation method is adapted to automatically choose these parameters. The method is illustrated numerically on a number of integral equations of the first kind.