Newton's Method for Convex Operators and Applications

Main Article Content

Octav Olteanu

Abstract

This review work presents the general statement of a variant of Newton's method for convex monotone operators and its applications. We consider the estimation of the absolute error too. One makes the connection to the contraction principle. One of the applications is approximating  where a positive selfadjoint operator is acting on a Hilbert space. One works with “global” convex monotone operators. For the local approach, we mention appropriate references.

Article Details

References

  1. Argyros, I. K., On the convergence and applications of Newton -like methods for analytic operators, J. Appl. Math. & Computing, 10, 1-2 (2002), 41-50.
  2. Balan, V., Olteanu, A. & Olteanu, O., some applications, Romanian Journal of Pures and Applied Mathematics, 51, 3 (2006), 277-290.
  3. Cristescu, R., Ordered Vector Spaces and Linear Operators, Academiei, Bucharest, and Abacus Press, Tunbridge Wells, Kent, 1976.
  4. Kantorovich, L. V. & Akilov, G. P., Functioanal Analysis, Scientific and Encyclopedic Publishing House, Bucharest, 1986 (in Romanian).
  5. J. M., Olteanu, A. & Olteanu, O., Applications of Newton convex monotone operators, Mathematical Reports, 7(57), 3 (2005), 219-231.
  6. Olteanu, O. & Simion, Gh., A new geometric aspect of the implicit function principle and method for operators. Mathematical Reports 5 (55), 1 (2003), 61-84.