登入選單
返回Google圖書搜尋
Numerical Methods for Roots of Polynomials - Part II
J.M. McNameeV.Y. Pan
其他書名
Chapter 9. Methods Involving Second or Higher Derivatives
出版Elsevier Inc. Chapters, 2013-07-19
主題Mathematics / Mathematical AnalysisMathematics / AppliedMathematics / GeneralMathematics / Algebra / GeneralMathematics / Calculus
ISBN01280769929780128076996
URLhttp://books.google.com.hk/books?id=5WF1DAAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋Whereas Newton’s method involves only the first derivative, methods discussed in this chapter involve the second or higher. The “classical” methods of this type (such as Halley’s, Euler’s, Hansen and Patrick’s, Ostrowski’s, Cauchy’s and Chebyshev’s) are all third order with three evaluations, so are slightly more efficient than Newton’s method. Convergence of some of these methods is discussed, as well as composite variations (some of which have fairly high efficiency). We describe special methods for multiple roots, simultaneous or interval methods, and acceleration techniques. We treat Laguerre’s method, which is known to be globally convergent for all-real-roots. The Cluster-Adapted Method is useful for multiple or near-multiple roots. Several composite methods are discussed, as well as methods using determinants or various types of interpolation, and Schroeder’s method.