Algorithms for Finding Zeros of Functions (UMAP)

This unit discusses methods for finding the zeros of real valued functions of a real variable. It begins with the classical methods of bisection, secant and Newton, and discusses their strong points and limitations. It concludes with an algorithm that combines the bisection and secant methods to bring out their best features. Students learn standard bisection, secant, and Newton root finding methods, their strong points and limitations.

Table of Contents:

1. EXISTENCE QUESTIONS

2. THE BISECTION METHOD

3. ROUNDOFF PROBLEMS

4. SOME LINEARIZATION METHODS

5. RATES OF CONVERGENCE

6. A PRACTICAL ALGORITHM

7. REFERENCES

8. ANSWERS TO EXERCISES