Root Finding
Numerical Methods with Computer Application Page 1
, ROOT FINDING
Different Methods used for Root Finding
A. Bisection Method
The division of a curve, figure or an interval in two equal parts
Figure 1.1:
y
X1 X2
x
Procedure: Root (X3)
1. [x1, x2 ] get x3 using the formula: x3 = (x1 + x2) ; x3 ≠ 0
2
2. Evaluate ε ≥ f(x3); ε = error threshold
3. Check which half contains solution:
Figure 1.2 Figure 1.3
or
X1 X3 X2 X1 X3 X2
4. Use X3 as the new endpoint of the range that contains the solution.
Numerical Methods with Computer Application Page 2
Numerical Methods with Computer Application Page 1
, ROOT FINDING
Different Methods used for Root Finding
A. Bisection Method
The division of a curve, figure or an interval in two equal parts
Figure 1.1:
y
X1 X2
x
Procedure: Root (X3)
1. [x1, x2 ] get x3 using the formula: x3 = (x1 + x2) ; x3 ≠ 0
2
2. Evaluate ε ≥ f(x3); ε = error threshold
3. Check which half contains solution:
Figure 1.2 Figure 1.3
or
X1 X3 X2 X1 X3 X2
4. Use X3 as the new endpoint of the range that contains the solution.
Numerical Methods with Computer Application Page 2
