Exercises on the bisection method

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Exercises on the bisection method


Numerical analysis > Exercises on the bisection method

Exercise 1[edit]

  • Write a Octave/MATLAB function for the bisection method. The function takes as arguments the function , the extrema of the interval and , the tolerance and the maximum number of iterations.
  • Consider the function in .
    1. How many roots are there in this interval?
    2. Theoretically, how many iterations are needed to find a solution?
    3. With , how many iterations are needed? Does the numerical result satisfy this condition?
    4. With , how many iterations are needed? Does the numerical result satisfy this condition?

Exercise 2[edit]

  • Consider the function in .
    1. Show the existence and uniqueness of the root .
    2. Given the tolerance , how many iterations are needed?
    3. Consider the restriction of the interval to . In this case how many iterations are needed?
    4. With the aid pf the Octave/MATLAB function of exercise 1, compute the root of the function.
    5. Compute the solution with precision e consider it as the exact solution. Then considering , draw a logarithmic plot to represent the average error and the actual error. Comment.

Exercise 3[edit]

Show that the sequence defined by the bisection method with we have

.