A THIRD-ORDER VARIANT OF NEWTON-SECANT METHOD FINDING A MULTIPLE ZERO

• 발행기관: 충청수학회
• 저자명: Young Ik Kim Sang Deok Lee
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 23, No. 4, 845~852쪽, 전체 8쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2010.12.30

영문 초록

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.

목차

1. Introduction

2. Convergence analysis

3. Algorithm, numerical results and discussions

References