학술저널
A THIRD-ORDER VARIANT OF NEWTON-SECANT METHOD FINDING A MULTIPLE ZERO
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 23, No. 4
-
2010.12845 - 852 (8 pages)
- 2
A nonlinear algebraic equation f(x) = 0 is consid-ered to ¯nd a root with integer multiplicity m ¸ 1. A variant of Newton-secant method for a multiple root is proposed below: for n = 0; 1; 2... It is shown that the method has third-order convergence and its asymptotic error constant is expressed in terms of m. Numeri-cal examples successfully veri¯ed the proposed scheme with high-precision Mathematica programming.
1. Introduction
2. Convergence analysis
3. Algorithm, numerical results and discussions
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