Quantitative Finance

Numerical Methods

Newton Raphson Method

         

Let f(x)=x372x220. f(x) = x^3 - 72x - 220. Given that f(x)=0f(x)=0 has a root near x=12, x = 12, compute x1 x_1 by using Newton-Raphson method starting with x0=12.x_0=12.

By using the Newton-Raphson method, find the positive root of the following quadratic equation correct to 5 5 significant figures: x2+9x5=0. x^2 + 9x - 5 = 0.

Start with x0=2.2. x_0 = 2.2.

Use the Newton-Raphson method, correct to 5 5 significant figures, to get the root near x=2 x = 2 of the equation f(x)=x33x8. f(x) = x^3 - 3x - 8.

The equation f(x)=4ex12 f(x) = 4e^x - 12 has a root near x=1. x = 1. Use the Newton-Raphson method to calculate the root correct to 5 5 significant figures.

Let f(x)=4x28. f(x) = 4 x^2 - 8. Which of the following is the correct representation of xn+1 x_{n+1} that Newton-Raphson method leads to?

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