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.