The document outlines the secant method for finding roots of non-linear equations, describing it as an efficient close-bracketing method. It explains the algorithm in a series of steps, starting with the selection of two initial values and iterative substitution based on function evaluations. A key aspect is determining the new bounds for the next iteration based on the signs of the function values at chosen points.

1. Finding Roots of Non-Linear
Equations using Secant Method
Compiled by:
Engr. Luigi Carlo M. De Jesus

2. Definition
• It is one of the most efficient way of
close bracketing method in root finding

3. Equation
• Derived from the point slope form
formula

4. Algorithm

5. Step 1
• Guess two values of x wherein f(Xa)<0 and f(Xb)>0

6. Step 2
• Substitute both values on the formula given
• Note: Xa is the same as Xn-2
Xb is the same as Xn-1
Xc is the same as Xn

7. Step 3
• If f(Xa) * f(Xc) < 0, then make Xc the new Xb in the next iteration,
otherwise make Xa the new Xb
• Note: If f(Xc) is approximately equal to 0, then Xc is the root