1. Secant Method Civil Engineering Majors Authors: Autar Kaw, Jai Paul http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates 07/28/10 http://numericalmethods.eng.usf.edu

2. Secant Method http://numericalmethods.eng.usf.edu

3. Secant Method – Derivation http://numericalmethods.eng.usf.edu Newton’s Method Approximate the derivative Substituting Equation (2) into Equation (1) gives the Secant method (1) (2) Figure 1 Geometrical illustration of the Newton-Raphson method.

4. Secant Method – Derivation http://numericalmethods.eng.usf.edu The Geometric Similar Triangles Figure 2 Geometrical representation of the Secant method. The secant method can also be derived from geometry: can be written as On rearranging, the secant method is given as

5. Algorithm for Secant Method http://numericalmethods.eng.usf.edu

6. Step 1 http://numericalmethods.eng.usf.edu Calculate the next estimate of the root from two initial guesses Find the absolute relative approximate error

10. Example 1 Cont. http://numericalmethods.eng.usf.edu Figure 3 Graph of the function f(x).

12. Example 1 Cont. http://numericalmethods.eng.usf.edu Figure 4 Graph of the estimated root after Iteration 1.

15. Example 1 Cont. http://numericalmethods.eng.usf.edu Figure 5 Graph of the estimate root after Iteration 2.

18. Example 1 Cont. http://numericalmethods.eng.usf.edu Figure 6 Graph of the estimate root after Iteration 3.

21. Drawbacks http://numericalmethods.eng.usf.edu Division by zero

22. Drawbacks (continued) http://numericalmethods.eng.usf.edu Root Jumping