TY - JOUR
T1 - Quadrature Based Optimal Iterative Methods with Applications in High-Precision Computing
AU - Sanjay Kumar Khattri
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 592
EP - 601
PY - 2012
DA - 2012/05
SN - 5
DO - http://doi.org/10.4208/nmtma.2012.m1114
UR - https://global-sci.org/intro/article_detail/nmtma/5951.html
KW - Iterative methods, fourth order, eighth order, quadrature, Newton, convergence, nonlinear, optimal.
AB - <p style="text-align: justify;">We present a simple yet effective and applicable scheme, based on quadrature, for constructing optimal iterative methods. According to the, still unproved, Kung-Traub conjecture an optimal iterative method based on $n+1$ evaluations could achieve a maximum convergence order of $2^n$. Through quadrature, we develop optimal iterative methods of orders four and eight. The scheme can further be applied to develop iterative methods of even higher orders. Computational results demonstrate that the developed methods are efficient as compared with many well known methods.</p>