  We introduce concepts of "recursive polynomial remainder sequence (PRS)" and
"recursive subresultant," and investigate their properties. In calculating PRS,
if there exists the GCD (greatest common divisor) of initial polynomials, we
calculate "recursively" with new PRS for the GCD and its derivative, until a
constant is derived. We call such a PRS a recursive PRS. We define recursive
subresultants to be determinants representing the coefficients in recursive PRS
by coefficients of initial polynomials. Finally, we discuss usage of recursive
subresultants in approximate algebraic computation, which motivates the present
work.
