iteration

Consider the following recursive iteration scheme for different values of variable P with the initial guess $x_1 = 1$: $x_{n+1} = \frac{1}{2} (x_n + \frac{P}{x_n})$, $n = 1, 2, 3,...

Consider the following recursive iteration scheme for different values of variable P with the initial guess x 1 = 1: $${x_{n + 1}} = {1 \over 2}\left( {{x_n} + {P \over {{x_n}}}} \...

In Newton-Raphson iterative method, the initial guess value $$\left( {{x_{ini}}} \right)$$ is considered as zero while finding the roots of the equation: $$\,f\left( x \right) = -...

The square root of a number $$N$$ is to be obtained by applying the Newton $$-$$ Raphson iteration to the equation $$\,{x^2} - N = 0.\,\,$$ If $$i$$ denotes the iteration index, th...

The Newton-Raphson iteration $${x_{n + 1}} = {1 \over 2}\left( {{x_n} + {R \over {{x_n}}}} \right)$$ can be used to compute

The following equation needs to be numerically solved using the Newton $$-$$ Raphson method $${x^3} + 4x - 9 = 0.\,\,$$ The iterative equation for this purpose is ($$k$$ indicates...

Given $$a>0,$$ we wish to calculate its reciprocal value $${1 \over a}$$ by using Newton - Raphson method for $$f(x)=0.$$ For $$a=7$$ and starting with $${x_0} = 0.2\,\,$$ the firs...

Let $$\,\,f\left( x \right) = x - \cos \,x.\,\,\,$$ Using Newton-Raphson method at the $$\,{\left( {n + 1} \right)^{th}}$$ iteration, the point $$\,{x_{n + 1}}$$ is computed from $...