This paper describes a non-linear structure-preserving ma
trix method for the com-
putation of the coefficients of an approximate greatest commo
n divisor (AGCD) of
degree
t
of two Bernstein polynomials
f
(
y
) and
g
(
y
). This method is applied to
a modified form
S
t
(
f, g
)
Q
t
of the
t
th subresultant matrix
S
t
(
f, g
) of the Sylvester
resultant matrix
S
(
f, g
) of
f
(
y
) and
g
(
y
), where
Q
t
is a diagonal matrix of com-
binatorial terms. This modified subresultant matrix has sig
nificant computational
advantages with respect to the standard subresultant matri
x
S
t
(
f, g
), and it yields
better results for AGCD computations. It is shown that
f
(
y
) and
g
(
y
) must be pro-
cessed by three operations before
S
t
(
f, g
)
Q
t
is formed, and the consequence of these
operations is the introduction of two parameters,
α
and
θ
, such that the entries of
S
t
(
f, g
)
Q
t
are non-linear functions of
α, θ
and the coefficients of
f
(
y
) and
g
(
y
). The
values of
α
and
θ
are optimised, and it is shown that these optimal values allo
w an
AGCD that has a small error, and a structured low rank approxi
mation of
S
(
f, g
),
to be computed.
CORE (COnnecting REpositories)
CORE (COnnecting REpositories)