Transcription of 2.2 Fixed-Point Iteration
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2.2 Fixed-Point Iteration
Fixed-Point Iteration 1. Basic Definitions A number is a fixed point for a given function if = . Root finding = 0 is related to Fixed-Point Iteration = . Given a root-finding problem = 0, there are many with fixed points at : Example: . + 3 .. If has fixed point at , then = ( ) has a zero at 2. Why study Fixed-Point Iteration ? 1. Sometimes easier to analyze 2. Analyzing Fixed-Point problem can help us find good root-finding methods A Fixed-Point Problem Determine the fixed points of the function = 2 2. 3. When Does Fixed-Point Iteration Converge?
• A number is a fixed point for a given function if = • Root finding =0 is related to fixed-point iteration = –Given a root-finding problem =0, there are many with fixed points at : Example: ≔ − ≔ +3 … If has fixed point at , then = − ( ) has
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