補充 數值方法 20061227 數值方法.

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1 補充 數值方法 數值方法

2 Objectives 數值方法，解決簡易工程問題之能力 線性聯立方程式求解 矩陣之行列式 非線性方程式求解 數值方法

3 線性聯立方程式求解 http://www.math.tku.edu.tw/~chinmei/Ulinear/PPT/1-1.ppt
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4 矩陣之行列式 http://www.math.tku.edu.tw/~chinmei/Ulinear/PPT/3-1.ppt
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5 非線性方程式求解 Bisection Method for finding Roots Iterative Recursive
TextBook of Hanly Chap 7 pp. 346 Recursive TextBook of Hanly Chap 10 pp. 550 數值方法

6 Iterative Approximations
Numerical Analysis: to develop algorithms for solving computational problems. Finding solutions to sets of equations, Performing operations on matrices, Finding roots of equations, and Performing mathematical integration. Many real-world problems can be solved by finding roots of equations. 數值方法

7 Six Roots for the Equation f(x) = 0
Case Study: Bisection Method for Finding Roots 數值方法

8 Function Parameters The bisection routine would be far more useful if we could call it to find a root of any function. Declaring a function parameter is accomplished by simply including a prototype of the function in the parameter list. 數值方法

9 Case Study: Bisection Method for Finding Roots
First, tabulate function values to find an appropriate interval in which to search for a root. 數值方法

10 Bisect this interval Three possibilities that wrise when the Iinterval [xleft, xright] is Bisected 數值方法

11 Epsilon A fourth possibility is that the length of the interval is less than Epsilon. Epsilon is a very small constant. In this case, any point in the interval is an acceptable root approximation. 數值方法

12 Finding a Function Root Using the Bisection Method Run demo
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13 Figure 7.11 Sample Run of Bisection Program with Trace Code Included
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14 Homework #10 Due: 2007/1/10 Determinant (矩陣之行列式 ) 作業要求:
此作業讓同學先將4x4矩陣簡化降階為3x3 (見參考資料1, 2), 再求之 作業要求: 1. 從檔案讀入一個4x4的矩陣x 2. 將此矩陣的每個數經由費氏數列Fibonacci Series轉換為另一個矩陣 3. 算出經由轉換後的矩陣之行列式 數值方法

15 Summary 數值方法