TY - JOUR
KW - Jarratt-type Methods
KW - Newton’s Method
KW - Banach Space
KW - Local Convergence
AU - Ioannis Argyros
AU - Daniel González
AB - We present a local convergence analysis for an improved Jarratt-type methods of order at least five to approximate a solution of a nonlinear equation in a Banach space setting. The convergence ball and error estimates are given using hypotheses up to the first Fréchet derivative in contrast to earlier studies using hypotheses up to the third Fréchet derivative. Numerical examples are also provided in this study, where the older hypotheses are not satisfied to solve equations but the new hypotheses are satisfied.
IS - Special Issue on Teaching Mathematics Using New and Classic Tools
M1 - 4
N2 - We present a local convergence analysis for an improved Jarratt-type methods of order at least five to approximate a solution of a nonlinear equation in a Banach space setting. The convergence ball and error estimates are given using hypotheses up to the first Fréchet derivative in contrast to earlier studies using hypotheses up to the third Fréchet derivative. Numerical examples are also provided in this study, where the older hypotheses are not satisfied to solve equations but the new hypotheses are satisfied.
PY - 2015
SP - 20
EP - 25
T2 - International Journal of Interactive Multimedia and Artificial Intelligence
TI - Local Convergence for an Improved Jarratt-type Method in Banach Space
UR - http://www.ijimai.org/JOURNAL/sites/default/files/files/2015/08/ijimai20153_4_4_pdf_25787.pdf
VL - 3
SN - 1989-1660
ER -