ON THE ORDER AND RATE OF CONVERGENCE FOR PSEUDO-SECANT-NEWTON’S METHOD LOCATING A

• 발행기관: 충청수학회
• 저자명: Young Ik Kim
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 19, No. 2, 1~7쪽, 전체 7쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2006.06.30

영문 초록

By combining the classical Newton’s method with the pseudo-secant method, pseudo-secant-Newton’s method is constructed and its order and rate of convergence are investigated. Given a function f : R → R that has a simple real zero α and is sufficiently smooth in a small neighborhood of α, the convergence behavior is analyzed near α for pseudo-secant-Newton’s method. The order of convergence is shown to be cubic and the rate of convergence is proven to be . Numerical experiments show the validity of the theory presented here and are confirmed via high-precision programming in Mathematica.

목차

1.. Introduction and Preliminaries

2.. Algorithm, numerical results and discussions