But do you really know the roots? You do know the roots of the polynomial q=:1;(i.20),20.0001 , but the roots of the polynomial p. q are a different matter. Is it possible to represent p. q in IEEE 64-bit floating point to get good answers for p. p. q ?
A warning about a polynomial root finder should say something to the effect that PROOT finding (by any root finder) is extremely sensitive to the coefficients. Vide the Wilkinson monster. ----- Original Message ----- From: John Randall <[EMAIL PROTECTED]> Date: Sunday, July 27, 2008 15:58 Subject: Re: [Jprogramming] Roots robustness? To: Programming forum <[email protected]> > Roger Hui wrote: > > How do you know that those are not the right answers? > > http://en.wikipedia.org/wiki/Wilkinson_polynomial > > Because I know the roots. Wilkinson's polynomial comes > from perturbing a > coefficient after the polynomial is expanded. > > >From the practical point of view: > > roots=: >@(1&{)@p. > q=:1;(i.20),20.0001 > p=:p. q > r=:roots p > > >./|p&p. r > 2.8237e14 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
