Question

Find an appropriate root of x^3 + 2x^2 − 5 = 0 in [1,2 ] with 10^(−5) accuracy by
i) Newton Raphson Method
ii) Secant Method
What conclusions can you draw from here about the two methods?

Answer 1

Question #65681, Math / Other

Find an appropriate root of $x^3 + 2x^2 - 5 = 0$ in $[1,2]$ with $10^(-5)$ accuracy by

i) Newton Raphson Method

ii) Secant Method

What conclusions can you draw from here about the two methods?

Answer.

i) $x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)} = x_n - \frac{x_n^3 + 2x_n^2 - 5}{3x_n^2 + 4x_n}$

So, with $10^{-5}$ accuracy $x = 1.24190$.

ii) $x_{n+2} = x_{n+1} - \frac{f(x_{n+1})(x_{n+1} - x_n)}{f(x_{n+1}) - f(x_n)}$

So, with $10^{-5}$ accuracy $x = 1.24190$.

The Newton-Raphson Method converges better.

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