2/18/17

HW3/README.md

@@ -11,8 +11,8 @@
     c. Copy your `projectile.m` function into the 'roots_and_optimization' folder.
     *Disable the plotting routine for the solvers*
 
-    d. 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 m, with an initial speed of 1.5 m/s. 
+    d. Use the four solvers `falsepos.m`, `bisect.m`, `newtraph.m` and `mod_secant.m`
+    to solve for the angle needed to reach h=1.72 m, with an initial speed of 15 m/s. 
 
     e. The `newtraph.m` function needs a derivative, calculate the derivative of your
     function with respect to theta, `dprojectile_dtheta.m`. This function should
@@ -29,7 +29,7 @@
         | solver | initial guess(es) | ea | number of iterations|
         | --- | --- | --- | --- |
         |falsepos   |  |  |  |
-        |incsearch  |  |  |  |
+        |bisect     |  |  |  |
         |newtraph   |  |  |  |
         |mod_secant |  |  |  |
         ```
@@ -49,7 +49,7 @@ using the numerical solvers, `newtraph.m` and `mod_secant.m`, there are certain
 guesses that do not converge. 
 
     a. Calculate the first 5 iterations for the Newton-Raphson method with an initial
-    guess of x_i=2. 
+    guess of x_i=2 for f(x)=x*exp(-x^2).
 
     b. Add the results to a table in the `README.md` with:
 
@@ -70,5 +70,4 @@ guesses that do not converge.
     'divergence' to 'convergence')
 
 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](https://goo.gl/forms/UJBGwp0fQcSxImkq2)
+copy and paste the "clone URL" into the following Google Form [Homework 3](https://goo.gl/forms/UJBGwp0fQcSxImkq2)

README.md

@@ -74,8 +74,8 @@ general, I will not post homework solutions.
 |3|1/31||Consistent Coding habits|
 |   |2/2|5|Root Finding| 
 |4|2/7|6|Root Finding con’d|      
-|   |2/9|7|Optimization|      
-|5|2/14||Intro to Linear Algebra|
+|   |2/9|7| **Snow Day**|      
+|5|2/14|| Optimization |
 |   |2/16|8|Linear Algebra|
 |6|2/21|9|Linear systems: Gauss elimination|
 |   |2/23|10|Linear Systems: LU factorization|

lecture_08/.ipynb_checkpoints/lecture_08-checkpoint.ipynb

@@ -0,0 +1,6 @@
+{
+ "cells": [],
+ "metadata": {},
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

lecture_08/goldmin.m

@@ -0,0 +1,36 @@
+function [x,fx,ea,iter]=goldmin(f,xl,xu,es,maxit,varargin)
+% goldmin: minimization golden section search
+%   [x,fx,ea,iter]=goldmin(f,xl,xu,es,maxit,p1,p2,...):
+%     uses golden section search to find the minimum of f
+% input:
+%   f = name of function
+%   xl, xu = lower and upper guesses
+%   es = desired relative error (default = 0.0001%)
+%   maxit = maximum allowable iterations (default = 50)
+%   p1,p2,... = additional parameters used by f
+% output:
+%   x = location of minimum
+%   fx = minimum function value
+%   ea = approximate relative error (%)
+%   iter = number of iterations
+if nargin<3,error('at least 3 input arguments required'),end
+if nargin<4|isempty(es), es=0.0001;end
+if nargin<5|isempty(maxit), maxit=50;end
+phi=(1+sqrt(5))/2;
+iter=0;
+while(1)
+  d = (phi-1)*(xu - xl);
+  x1 = xl + d;
+  x2 = xu - d;
+  if f(x1,varargin{:}) < f(x2,varargin{:})
+    xopt = x1;
+    xl = x2;
+  else
+    xopt = x2;
+    xu = x1;
+  end
+  iter=iter+1;
+  if xopt~=0, ea = (2 - phi) * abs((xu - xl) / xopt) * 100;end
+  if ea <= es | iter >= maxit,break,end
+end
+x=xopt;fx=f(xopt,varargin{:});