Practice question · Put in order
Order the steps in one iteration of Newton's method for root-finding.
- Compute the next iterate:
- Evaluate f() and f'()
- Start with an initial guess close to the root
- Repeat until |₊₁ − | is smaller than the desired tolerance
Hints
- Each step needs both the function value and the slope at the current guess.
- The updated guess is produced last and feeds the next iteration.
Show the answer
- Start with an initial guess close to the root
- Evaluate f() and f'()
- Compute the next iterate:
- Repeat until |₊₁ − | is smaller than the desired tolerance
Why
Newton's method has quadratic convergence near simple roots.
Practise Graphs, approximation, and numerical sense
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