Generation of orthogonal rational functions by procedures for structured matrices

The problem of computing recurrence coefficients sequences rational functions orthogonal with respect to a discrete inner product is formulated as an inverse eigenvalue for pencil Hessenberg matrices. Two procedures are proposed solve this problem, via the Arnoldi iteration and updating procedure using unitary similarity transformations. latter shown be numerically stable. This both generalized by considering biorthogonal bilinear form. leads tridiagonal A implies short relations functions, which more efficient than case. However solving must rely on nonunitary operations might not