翻訳と辞書 Words near each other ・ Simplicial group ・ Simple Pleasure ・ Simple Pleasures ・ Simple Pleasures (Alison Brown album) ・ Simple Pleasures (Bobby McFerrin album) ・ Simple polygon ・ Simple polytope ・ Simple Power ・ Simple precedence grammar ・ Simple precedence parser ・ Simple present ・ Simple prioritization ・ Simple programmable logic device ・ Simple public-key infrastructure ・ Simple random sample ・ Simple rational approximation ・ Simple resolution ・ Simple ring ・ Simple Science ・ Simple Sensor Interface protocol ・ Simple sequence length polymorphism ・ Simple series ・ Simple Service Discovery Protocol ・ Simple set ・ Simple shear ・ Simple Simon ・ Simple Simon (1922 film) ・ Simple Simon (2010 film) ・ Simple Simon (INXS song) ・ Simple Simon (musical) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Simple rational approximation ： ウィキペディア英語版 Simple rational approximation Simple rational approximation (SRA) is a subset of interpolating methods using rational functions. Especially, SRA interpolates a given function with a specific rational function whose poles and zeros are simple, which means that there is no multiplicity in poles and zeros. Sometimes, it only implies simple poles. The main application of SRA lies in finding the zeros of secular functions. A divide-and-conquer algorithm to find the eigenvalues and eigenvectors for various kinds of matrices is well known in numerical analysis. In a strict sense, SRA implies a specific interpolation using simple rational functions as a part of the divide-and-conquer algorithm. Since such secular functions consist of a series of rational functions with simple poles, SRA is the best candidate to interpolate the zeros of the secular function. Moreover, based on previous researches, a simple zero that lies between two adjacent poles can be considerably well interpolated by using a two-dominant-pole rational function as an approximating function. == One-point third-order iterative method: Halley's formula == The origin of the interpolation with rational functions can be found in the previous work done by Edmond Halley. Halley's formula is known as one-point third-order iterative method to solve $\backslash ,f(x)=0$ by means of approximating a rational function defined by :$h(z)=\backslash frac+c.$ We can determine a, b, and c so that :$h^(x)=f^(x),\; \backslash qquad\; i=0,1,2.$ Then solving $\backslash ,h(z)=0$ yields the iteration :$x\_=x\_-\backslash frac\; \backslash left(\}\}\backslash right).$ This is referred to as Halley's formula. This ''geometrical interpretation'' $h(z)$ was derived by Gander(1978), where the equivalent iteration also was derived by applying Newton's method to :$g(x)=\backslash frac\{\backslash sqrt\{f\text{'}(x)\}\}=0.$ We call this ''algebraic interpretation'' $g(x)$ of Halley's formula. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Simple rational approximation」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.