2.5.1 - How Fixed-Point Iteration Works
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Practice Questions
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What is fixed-point iteration?
💡 Hint: Think about how we transform equations.
State one advantage of fixed-point iteration.
💡 Hint: Consider the mathematical complexity needed.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the first step in fixed-point iteration?
💡 Hint: Think about the equation structure.
Does fixed-point iteration guarantee convergence for all functions?
💡 Hint: Recall the conditions for convergence.
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Challenge Problems
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Propose a g(x) function for f(x) = cos(x) - x, check if it converges using a suitable x₀.
💡 Hint: Analyze the cosine function derivative.
Set up and perform fixed-point iteration for f(x) = e^x - 3x^2; what initial guess leads to rapid convergence?
💡 Hint: Use properties of exponentials for rapid convergence.
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