- #1

Alphax

- 11

- 0

## Homework Statement

Use Newton's method with x1 = 1 to find the root of the equation x3 - x = 1 to correct six decimal places.

Do the question again with x1 = 0.6

Do the question again with x1 = 0.57

You probably need to do it in an excel sheet. With each try, it takes longer to find root of the equation. My question is why Newton's method is so sensitive to the value of initial approximation.

## Homework Equations

## The Attempt at a Solution

I am not seeking the answers to Newton's method. I am trying to understand why Newton's method is sensitive to inaccurate initial approximation. For this problem, 1 is much closer to the root of the equation than 0.6 or 0.57, and this is the reason why I was able to find the answer faster. As the initial approximation is further from the root of the equation, the answer takes longer time to solve.

So, why is the value of initial approximation have an impact on the time it takes to solve the equation.