[sci.math] Bounds on a Polynomial - looking for a better method.

dilip@ncst.ernet.in (DR Khandekar) (09/06/90)

We, at the Graphics and CAD Divn. of NCST, Bombay, India, are working on a 
surface modeling system involving B-Spline techniques. We are in need of a 
method to determine a tight bound on absolute value of a polynomial f defined
over a parameter u, i.e., to find Uf such that,

   Uf   >=    max    | f(u) |
            0<=u<=1

and also to find upper and lower bounds Umax,Umin such that,

   Umin  <=  f(u)  <=  Umax,   for 0 <= u <= 1.

Does anyone know about a method of determining the above mentioned bounds 
that gives better results than, but having same time complexity as, the method
involving Bezier control points. We need it for Piecewise linear approximation
of a B-Spline curve and for subdivision algorithms, eg, intersection, etc.

Please respond by direct e-mail at the following addresses:

      dilip@ncst.ernet.in    or  uunet!shakti!dilip
      gopal@ncst.ernet.in    or  uunet!shakti!gopal

Thanks in advance,

Dilip Khandekar

Graphics and CAD Divn.,
National Center for Software Technology,
Juhu, Bombay, INDIA.