We present a computational procedure for generating formally orthogonal polynomials associated with a given bilinear Hankel form with rectangular matrix-valued moments. Our approach covers the most general case of moments of any size and is not restricted to square moments. Moreover, our algorithm has a built-in deflation procedure to handle linearly dependent or almost linearly dependent columns and rows of the block Hankel matrix associated with the bilinear form. Possible singular or close-to-singular leading principal submatrices of the deflated block Hankel matrix are avoided by means of look-ahead techniques. Applications of the computational procedure to eigenvalue computations, reduced-order modeling, the solution of multiple linear systems, and the fast solution of block Hankel systems are also briefly described. © 2001 Elsevier Science B.V.
Freund, R. W. (2001). Computation of matrix-valued formally orthogonal polynomials and applications. Journal of Computational and Applied Mathematics, 127(1–2), 173–199. https://doi.org/10.1016/S0377-0427(00)00505-7