Iteration Revisited Examples from a General Theory

  • Authors:

  • Poul Wulff Pedersen

  • Affiliations:

  • -

  • Venue:
  • ICCS '02 Proceedings of the International Conference on Computational Science-Part II
  • Year:
  • 2002

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Abstract

For 'any' equation F(x) = 0 withan isolated solution x* which we want to compute, it will be shown that quantities pn can be defined and computed so that xpn+1 := xpn + pn 驴 F(xpn) will 'converge' with'an y' speed needed, i.e. starting withan xp0 in a neigbourhood of x*, xpN will for for some small value of N give x* within the precision you need. And it will do so even if the 'standard' iteration xn+1 := xn + F(xn) is divergent.