The elementary iterative-recipe character of continued fractions
makes them more than just an analytic concept or a numerical tool
- they pose a challenge for generalizations. With matrix continued
fractions being the best known example of such a generalization, a
doubly challenging task is a vectorial generalization. One of
possibilities is proposed by the authors. Their important
inspiration may be traced to the transition from real numbers to
complex domain, and their strong point may be found in analogies.
They succeeded in finding them in the domain of polynomial-type
functions of a vector or recurrences and Christoffel-Darbox-type
identities. Interesting observations are made about convergence.
Via a few numerical examples, new questions (concerning, e.g.,
quadrature formulae) are shown to emerge.




MR2044762 Haydock, Roger ; Nex, C. M. M. ; Wexler, Geoffrey .
Vector continued fractions using a generalized inverse. J. Phys. A
37 (2004), no. 1, 161--172.