  By introducing some special bi-orthogonal polynomials, we derive the
so-called discrete hungry quotient-difference (dhQD) algorithm and a system
related to the QD-type discrete hungry Lotka-Volterra (QD-type dhLV) system,
together with their Lax pairs. These two known equations can be regarded as
extensions of the QD algorithm. When this idea is applied to a higher analogue
of the discrete-time Toda (HADT) equation and the quotient-quotient-difference
(QQD) scheme proposed by Spicer, Nijhoff and van der Kamp, two extended systems
are constructed. We call these systems the hungry forms of the higher analogue
discrete-time Toda (hHADT) equation and the quotient-quotient-difference (hQQD)
scheme, respectively. In addition, the corresponding Lax pairs are provided.
