diff --git a/HW3/README.html b/HW3/README.html deleted file mode 100644 index 950e6d3..0000000 --- a/HW3/README.html +++ /dev/null @@ -1,60 +0,0 @@ - - - - - - - - - - -

Homework #3

-

due 2/15/17 by 11:59pm

-
    -

  1. Create a new github repository called ‘roots_and_optimization’.

    -
      -

    1. Add rcc02007 and pez16103 as collaborators.

      2. -

    2. Clone the repository to your computer.

      3. -

    3. Copy your projectile.m function into the ‘roots_and_optimization’ folder. Disable the plotting routine for the solvers

      4. -

    4. Use the four solvers falsepos.m, incsearch.m, newtraph.m and mod_secant.m to solve for the angle needed to reach h=1.72, with an initial speed of 1.5 m/s.

      5. -

    5. The newtraph.m function needs a derivative, calculate the derivative of your function with respect to theta, dprojectile_dtheta.m. This function should output d(h)/d(theta).

      6. -

    6. In your README.md file, you will document the following under the heading # Homework #3:

      -
        -
      1. Compare the number of iterations that each function needed to reach an accuracy of 0.00001%. Include a table in your README.md with:
        2. -
      -
      | solver | initial guess(es) | ea | number of iterations|
-| --- | --- | --- | --- |
-|falsepos   |  |  |  |
-|incsearch  |  |  |  |
-|newtraph   |  |  |  |
-|mod_secant |  |  |  |
      -
        -
      1. Compare the convergence of the 4 methods. Plot the approximate error vs the number of iterations that the solver has calculated. Save the plot as convergence.png and display the plot in your README.md with:
        2. -
      -

      ![Plot of convergence for four numerical solvers.](convergence.png)

      -
        -
      1. In the README.md provide a description of the files used to create the table and the convergence plot.
        2. -
      7. -
    2. -

  2. The Newton-Raphson method and the modified secant method do not always converge to a solution. One simple example is the function f(x) = x*exp(-x^2). The root is at 0, but using the numerical solvers, newtraph.m and mod_secant.m, there are certain initial guesses that do not converge.

    -
      -

    1. Calculate the first 5 iterations for the Newton-Raphson method with an initial guess of x_i=2.

      2. -

    2. Add the results to a table in the README.md with:

      3. -
    -
    ### divergence of Newton-Raphson method
-
-| iteration | x_i | approx error |
-| --- | --- | --- |
-| 0 | 2 | n/a |
-| 1 |   |     |
-| 2 |   |     |
-| 3 |   |     |
-| 4 |   |     |
-| 5 |   |     |
    -
      -
    1. Repeat steps a-b for an initial guess of 0.2. (But change the heading from ‘divergence’ to ‘convergence’)
      2. -
    3. -

  3. Commit your changes to your repository. Sync your local repository with github. Then copy and paste the “clone URL” into the following Google Form Homework #3

    4. -
- -