On generalised Gaussian quadratures

C.F. Borges proposed to use quadrature rules of Gaussian type for simultaneous calculation of integrals with respect to several weights. This approach is especially beneficial when calculation of the integrand is a relatively expensive operation. Typical applications however only deal with AT-systems of weights. With our co-authors, we are interested in studying other systems of weights, which seem to have nice applications. In particular, we study Gaussian-type quadrature rules for certain Angelesco systems and consider properties of their averaged versions.