6_Newton-Raphson_method.pdf

17 figure 5 estimate of the root for the first

  • No School
  • AA 1
  • 33

This preview shows page 17 - 28 out of 33 pages.

17 Figure 5 Estimate of the root for the first iteration.
Image of page 17

Subscribe to view the full document.

Example 1 Cont. % 90 . 19 100 06242 . 0 05 . 0 06242 . 0 100 1 0 1 x x x a 18 The absolute relative approximate error at the end of Iteration 1 is a The number of significant digits at least correct is 0, as you need an absolute relative approximate error of 5% or less for at least one significant digits to be correct in your result.
Image of page 18
Example 1 Cont. 06238 . 0 10 4646 . 4 06242 . 0 10 90973 . 8 10 97781 . 3 06242 . 0 06242 . 0 33 . 0 06242 . 0 3 10 .993 3 06242 . 0 165 . 0 06242 . 0 06242 . 0 ' 5 3 7 2 4 2 3 1 1 1 2 x f x f x x 19 Iteration 2 The estimate of the root is
Image of page 19

Subscribe to view the full document.

Example 1 Cont. 20 Figure 6 Estimate of the root for the Iteration 2.
Image of page 20
Example 1 Cont. % 0716 . 0 100 06238 . 0 06242 . 0 06238 . 0 100 2 1 2 x x x a 21 The absolute relative approximate error at the end of Iteration 2 is a The maximum value of m for which is 2.844. Hence, the number of significant digits at least correct in the answer is 2. m a 2 10 5 . 0
Image of page 21

Subscribe to view the full document.

Example 1 Cont. 06238 . 0 10 9822 . 4 06238 . 0 10 91171 . 8 10 44 . 4 06238 . 0 06238 . 0 33 . 0 06238 . 0 3 10 .993 3 06238 . 0 165 . 0 06238 . 0 06238 . 0 ' 9 3 11 2 4 2 3 2 2 2 3 x f x f x x 22 Iteration 3 The estimate of the root is
Image of page 22
Example 1 Cont. 23 Figure 7 Estimate of the root for the Iteration 3.
Image of page 23

Subscribe to view the full document.

Example 1 Cont. % 0 100 06238 . 0 06238 . 0 06238 . 0 100 2 1 2 x x x a 24 The absolute relative approximate error at the end of Iteration 3 is a The number of significant digits at least correct is 4, as only 4 significant digits are carried through all the calculations.
Image of page 24
Advantages and Drawbacks of Newton Raphson Method 25
Image of page 25

Subscribe to view the full document.

Advantages Converges fast (quadratic convergence), if it converges. Requires only one guess 26
Image of page 26
Drawbacks 27 1. Divergence at inflection points Selection of the initial guess or an iteration value of the root that is close to the inflection point of the function may start diverging away from the root in ther Newton-Raphson method.
Image of page 27

Subscribe to view the full document.

Image of page 28
  • Fall '19

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern