Remark on an equivalent relation in least square approximation

In this note it is shown that the least square inverse of the 2-D polynomial B(z
1
, z
2
) = b
00
+ b
mt
z
1
^m
z
2
^t
+ b
ns
z
1
ⁿ
z
2
^s
+ b
m+n, s+t
ċ z
1
^m+n
z
2
^s+t
with (nt - ms) ≠ 0 is stable. This extends the Shanks' conjecture for a larger class of 2-D polynomials.