East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
권호 표지
DOI QR코드

DOI QR Code

AN IMPROVED NEWTON-KANTOROVICH THEOREM AND INTERIOR POINT METHODS

  • Received : 2008.10.09
  • Accepted : 2009.04.08
  • Published : 2009.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

We use an improved Newton-Kantorovich theorem introduced in [2] to analyze interior point methods. Our approach requires less number of steps than before [5] to achieve a certain error tolerance for both Newton's and Modified Newton's methods.

Keywords

References

  1. I. K. Argyros, Advances in the Effciency of Computational Methods and Applications, World Scientific Publ. Co., River Edge, NJ, 2000.
  2. I. K. Argyros, On the Newton-Kantorovich hypothesis for solving equations, J. Comput. Appl. Math., 169 (2004), 315-332. https://doi.org/10.1016/j.cam.2004.01.029
  3. I. K. Argyros, A unifying local-semilocal convergence analysis and applications for two-point Newton like methods in Banach space, J. Math. Anal. Appl., 298 (2004), no. 2, 374-397. https://doi.org/10.1016/j.jmaa.2004.04.008
  4. L. V. Kantorovich, and G. P. Akilov, Functional Analysis in Normed Spaces, Pergamon Press, Oxford, 1982.
  5. F. A. Potra, The Kantorovich Theorem and interior point methods, Math. Program., 102 (2005), no. 1, Ser. A, 47-70. https://doi.org/10.1007/s10107-003-0501-8