A matrix algorithm towards solving the moment problem of Sobolev type

We propose a matrix algorithm which is the first step towards considering a given matrix as a moment matrix of Sobolev type in the diagonal form of an arbitrary (not necessarily finite) order on the real line or the unit circle. This continues our recent work [Proc. Amer. Math. Soc., 128 (2000) 2309] on the moment problem of Sobolev type and gives an alternative approach to what is in [J. Approx. Theory 100 (1999) 364].