Algorithms (Aug 2015)

Expanding the Applicability of a Third Order Newton-Type Method Free of Bilinear Operators

  • Sergio Amat,
  • Sonia Busquier,
  • Concepción Bermúdez,
  • Ángel Alberto Magreñán

DOI
https://doi.org/10.3390/a8030669
Journal volume & issue
Vol. 8, no. 3
pp. 669 – 679

Abstract

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This paper is devoted to the semilocal convergence, using centered hypotheses, of a third order Newton-type method in a Banach space setting. The method is free of bilinear operators and then interesting for the solution of systems of equations. Without imposing any type of Fréchet differentiability on the operator, a variant using divided differences is also analyzed. A variant of the method using only divided differences is also presented.

Keywords