《数值分析》课程PPT教学课件（英文版）Chapter 01 The Solution of Nonlinear Equations 1.1 Iteration for Solving x=g（x）

Chapter 1 The solution of nonlinear Equations f(a)=0

Chapter 1 The Solution of Nonlinear Equations f(x)=0

1.1 Iteration for Solving x=g(x)

1.1 Iteration for Solving x=g(x)

ppp p1=9(0 9(P Pk=9(k-1) Pk+1=9(k)

Example 1. 1. The iterative rule po 1 and pk+1= 1.001pk for k=0, 1,..pro- duces a divergent sequence. The first 100 terms look as follows: P1=1.0170=(1.001010001.00100 p2=1011=(1001)(1.0000001 3=1012=(1001)(1.002011.00300 p100=1.0019(1.001)(1.104012)=1.105116

1. 1. 1 Finding Fixed Points

1.1.1 Finding Fixed Points