TY - GEN
T1 - Derivative-free family of higher order root finding methods
AU - Hasan, Mohammed A.
PY - 2009
Y1 - 2009
N2 - Most higher order root finding methods require evaluation of a function and/or its derivatives at one or multiple points. There are cases where the derivatives of a given function are costly to compute. In this paper, higher order methods which do not require computation of any derivatives are derived. Asymptotic analysis has shown that these methods are approximations of root iterations. One of the main features of the proposed approaches is that one can develop multi-point derivative-free methods of any desired order. For lower order methods, these correspond to the Newton, and Ostrowski iterations. Several examples involving polynomials and entire functions have shown that the proposed methods can be applied to polynomial and non-polynomial equations.
AB - Most higher order root finding methods require evaluation of a function and/or its derivatives at one or multiple points. There are cases where the derivatives of a given function are costly to compute. In this paper, higher order methods which do not require computation of any derivatives are derived. Asymptotic analysis has shown that these methods are approximations of root iterations. One of the main features of the proposed approaches is that one can develop multi-point derivative-free methods of any desired order. For lower order methods, these correspond to the Newton, and Ostrowski iterations. Several examples involving polynomials and entire functions have shown that the proposed methods can be applied to polynomial and non-polynomial equations.
KW - Derivative free methods
KW - Halley's method
KW - Higher order methods
KW - Newton's method
KW - Order of convergence
KW - Ostrowski method
KW - Root iterations
KW - Root-finding
KW - Square root iteration
KW - Zeros of analytic functions
KW - Zeros of polynomials
UR - http://www.scopus.com/inward/record.url?scp=70449635919&partnerID=8YFLogxK
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U2 - 10.1109/ACC.2009.5160587
DO - 10.1109/ACC.2009.5160587
M3 - Conference contribution
AN - SCOPUS:70449635919
SN - 9781424445240
T3 - Proceedings of the American Control Conference
SP - 5351
EP - 5356
BT - 2009 American Control Conference, ACC 2009
T2 - 2009 American Control Conference, ACC 2009
Y2 - 10 June 2009 through 12 June 2009
ER -