=ADD=
=bibkey=
GC:1995a
=author=
Collins; George E.
=title=
Application of Quantifier Elimination to Solotareff's Approximation Problem
=number=
95-31
=year=
1995
=sponsor=
 Austrian Science Foundation, grant P8572-PHY. 
=url=
ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1995/95-31.ps.gz
=abstract=
Solotareff's approximation problem is that of obtaining
the best uniform approximation on the interval [-1,+1]
of a real polynomial of degree $n$ by one of degree
$n - 2$ or less.  Without loss of generalitywe take
the approximated polynomial to be $x^n + r x^{n-1}$,
$r \geq 0$.  We treat $r$ as a parameter and
seek to compute the coefficients of the best
approximations, for small fixed values of $n$, as
piecewise algebraic functions of $r$.  We succeed only
for $n \leq 4$, but also find that we can easily
compute the coefficients for $n = 5$ for fixed values
of $r$.  The results serve to display the capabilities
and limitations of our quantifier elimination program
{\bf qepcad}.  We also prove that the coefficients of
the best approximation, for any $n$, are continuous
functions of $r$.
=location=
2
=owner=
2
=source=
3
=reftype=
14