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2d-root-finding-with-newton-method's Introduction

Homework 1

00957016 高敬庭

[1.0, 1.0]疊代過程

格式 :
Iteration : (Start.x, Start.y)
alt text 對照上圖,由(1, 1)開始,第一次疊代結束後到(2, 1),最後收斂到(1.73205, 1),總共四個點。
alt text

x=-3~3, y=-3~3 共49點作為最初猜測

alt text 圖中右上角標示代表該顏色的點對應到的收斂結果,共有四個區域,從標示的上到下分別對應到座標中的左下、左上、右下和右上,點座標用黑色的則表示該點會發散。

誤差計算方式

alt text alt text
誤差計算使用2-norm的方式,呼叫方式如上圖,疊代過程請見附檔result.txt。

加入Perturbation (畫圖用原(-2, 0)表示)

  • Perturbation = 0.0001 alt text 如圖所示,第一次疊代後y值衝到5000,之後每次疊代y值會大約等於前次的一半,總共經過17次疊代後收斂於(-1.73205,1)
    alt text 其餘所有點的疊代過程參考result_pertubation.txt。

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