Suppose we want to estimate the fifth root of 80.5 using the Newton Raphson algo
ID: 2031128 • Letter: S
Question
Suppose we want to estimate the fifth root of 80.5 using the Newton Raphson algorithm. This is equivalent to solving the equation f(x) 5-80.5-0. A decent initial guess might be 2.5 since 25 32 and 3 243. For this particular function, work out what the update algorithm would be for the Newton Raphson algorithm and complete the expression below:* Now work through the Newton Raphson algorithm by hand to complete Table 1 for an initial guess of 2.5. Table 1: Estimate of 5th Root of 80.5. 5th Root Estimate Using Evaluate Accuracy: ° Number of Iterations. New ton Raphson X1-2.5 -Explanation / Answer
The equation to be solved using Newton raphson method is f(x)=x5-80.5=0 with an initial guess of 2.5
the update algorithm is xn+1=xn - f(xn)/f'(xn)
or, xn+1=xn - [(xn5-80.5)/5xn4]
x1=2.5
x2=2.5-[(2.55-80.5)/(5*2.54)]=2.412
x3=2.412-[(2.4125-80.5)/(5*2.4124)]=2.405
x4=2.405-[(2.4055-80.5)/(5*2.4054)]=2.405
Therefore, the root of equaation with initila guess of 2.5 is 2.405