Numerical Methods20805 marksNumerical: Secant method rootSecant method formula and derivation
Use secant method to estimate the root of the equation x2-5x+6=0, with initial estimate x1 = 4 and x2 = 2 (EPS=0.05).
Use secant method to estimate the root of the equation $x^2-5x+6=0$, with initial estimate $x_1 = 4$ and $x_2 = 2$ (EPS=0.05). [5]
- Equation: $f(x) = x^2 - 5x + 6$ - Initial estimates: $x1 = 4$, $x2 = 2$ - Tolerance: $\text{EPS} = 0.05$ Secant formula: $$x{n+1} = xn - f(xn)\cdot\frac{xn - x{n-1}}{f(xn) - f(x{n-1})}$$ Stopping criterion: $$\varepsilon = \left\frac{x{n+1} - xn}{x{n+1}}\right < 0.05$$ $$f(x1) = f(4) = 16 - 20 ...