TY - GEN

T1 - On the derivation of higher order root-finding methods

AU - Hasan, Mohammed A.

PY - 2007/12/1

Y1 - 2007/12/1

N2 - High order root-finding algorithms are constructed based on some canonical conditions and a generalized Taylor series. The convergence order is automatically determined using these canonical conditions. The proposed approaches resulted in deriving methods of any desired order including the Newton, Halley, and Ostrowski iterations. It is also shown that, when zeros are simple, higher order methods may be obtained by applying lower order methods such as Newton Iteration to new functions which have same zeros as the original function. These functions are constructed so that the first few derivatives beyond the first vanish. Several examples are given for constructing methods of higher order for computing the zeros of the entire function sin(z).

AB - High order root-finding algorithms are constructed based on some canonical conditions and a generalized Taylor series. The convergence order is automatically determined using these canonical conditions. The proposed approaches resulted in deriving methods of any desired order including the Newton, Halley, and Ostrowski iterations. It is also shown that, when zeros are simple, higher order methods may be obtained by applying lower order methods such as Newton Iteration to new functions which have same zeros as the original function. These functions are constructed so that the first few derivatives beyond the first vanish. Several examples are given for constructing methods of higher order for computing the zeros of the entire function sin(z).

KW - Halley's method

KW - Higher order methods

KW - Newton's method

KW - Order of convergence

KW - Ostrowski method

KW - Root-finding

KW - Square root iteration

KW - Zeros of analytic functions

KW - Zeros of polynomials

KW - rth root iterations

UR - http://www.scopus.com/inward/record.url?scp=46449091512&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=46449091512&partnerID=8YFLogxK

U2 - 10.1109/ACC.2007.4282965

DO - 10.1109/ACC.2007.4282965

M3 - Conference contribution

AN - SCOPUS:46449091512

SN - 1424409888

SN - 9781424409884

T3 - Proceedings of the American Control Conference

SP - 2328

EP - 2333

BT - Proceedings of the 2007 American Control Conference, ACC

T2 - 2007 American Control Conference, ACC

Y2 - 9 July 2007 through 13 July 2007

ER -