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Fixed-Point Iteration
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Last edited: Jul 23, 2025
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1. Background
2. Theory
2.1. The Basic Idea
2.2. Convergence Properties
2.3. Derivation of Fixed-Point Iteration
2.3.1. Existance of a fixed-point in the interval
2.3.2. Uniqueness of a fixed-point in the interval
2.3.3. Convergence
3. Extensions
3.1. From to
3.2. From to
3.3. The Banach Fixed-Point Theorem (in a nutshell)
3.4. Attracting Fixed-Points
4. Examples
4.1. Babylonian Method
4.2. Newton’s Method
5. Conclusion & Reference
Bichi Zhang
Hi, I am Bichy, an autonomous systems & robotics enthusiast. Welcome to my webpage!
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1. Background
2. Theory
2.1. The Basic Idea
2.2. Convergence Properties
2.3. Derivation of Fixed-Point Iteration
2.3.1. Existance of a fixed-point in the interval
2.3.2. Uniqueness of a fixed-point in the interval
2.3.3. Convergence
3. Extensions
3.1. From to
3.2. From to
3.3. The Banach Fixed-Point Theorem (in a nutshell)
3.4. Attracting Fixed-Points
4. Examples
4.1. Babylonian Method
4.2. Newton’s Method
5. Conclusion & Reference
