We consider the problem of generating the recursion coefficients of or-
thogonaf polynomials for a given weight function. The weight function
is assumed to he the weighted sum of weight functions, each supported
on its own interval. Some of these intervals may coincide, overlap or are
contiguous. We discuss three algon’thms. Two of them are based on
modified moments, whereas the other is based on an explicit expression
for the desired coefficients. Several examples, illustrating the numerical
pefiormance of the various methods, are presented.