Stability of the recurrent determination of matrix elements generated by products of orthogonal polynomials

The stability with respect to the initial data of the recurrence determination of matrices generated by products of polynomials, orthogonal in a finite or semi-infinite interval, is considered, and the increase of the computational error is studied. A procedure is given for the practical use of the estimates obtained. Sufficient conditions are obtained, both for stability with respect to the initial data, and for acceptable growth of the computational error, in terms of the coefficients of the recurrence relations for the polynomials. A special normalization is used for the studies of stability.