5.1.3.5. Fixed Point Iteration Method

Try these first

1. 1.

   Define Fixed Point Iteration Method.

   Hint

   Consider the purpose of approximating solutions.

2. 2.

   What is the main requirement for the function g(x)?

   Hint

   Think about convergence conditions.

3. 3.

   Which of the following best describes the Fixed Point Iteration Method?

   • A method requiring a derivative to find roots
   • A numerical technique involving iterative substitutions
   • A graphical approach to root finding

   Hint

   Think about its iterative nature.

4. 4.

   True or false: The Fixed Point Iteration Method can be applied to any equation.

   • True
   • False

   Hint

   Analyze the requirements for a function to converge.

5. 5.

   Given the equation x = x² - 2, apply Fixed Point Iteration with a starting guess of 1. Describe the steps and check for convergence.

   Hint

   Evaluate each value for convergence conditions.

6. 6.

   Construct a function g(x) from x - cos(x) = 0 and demonstrate using Fixed Point Iteration with initial guess 0.5.

   Hint

   Check the derivatives to confirm convergence.