A Remarkable Chord Iterative Method for Roots of Uncertain Multiplicity  

作　　者：I. Fried I. Fried(Department of Mathematics, Boston University, Boston, MA, USA)

机构地区：[1]Department of Mathematics, Boston University, Boston, MA, USA

出　　处：《Applied Mathematics》2016年第11期1207-1214,共9页应用数学（英文）

摘　　要：In this note we at first briefly review iterative methods for effectively approaching a root of an unknown multiplicity. We describe a first order, then a second order estimate for the multiplicity index m of the approached root. Next we present a second order, two-step method for iteratively nearing a root of an unknown multiplicity. Subsequently, we introduce a novel chord, or a two- step method, not requiring beforehand knowledge of the multiplicity index m of the sought root, nor requiring higher order derivatives of the equilibrium function, which is quadratically convergent for any , and then reverts to superlinear.In this note we at first briefly review iterative methods for effectively approaching a root of an unknown multiplicity. We describe a first order, then a second order estimate for the multiplicity index m of the approached root. Next we present a second order, two-step method for iteratively nearing a root of an unknown multiplicity. Subsequently, we introduce a novel chord, or a two- step method, not requiring beforehand knowledge of the multiplicity index m of the sought root, nor requiring higher order derivatives of the equilibrium function, which is quadratically convergent for any , and then reverts to superlinear.

关 键 词：Iterative Methods Unknown Root Multiplicity Two-Step Methods 

分 类 号：O17[理学—数学]