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--- gibson:teaching:fall-2013:math445:lab5 [2013/09/23 19:30]
gibson
+++ gibson:teaching:fall-2013:math445:lab5 [2013/10/03 05:42] (current)
gibson
@@ Line 31: / Line 31: @@
 <latex>
 f\left(\begin{array}{c} x_1 \\ x_2 \end{array}}\right) =
-\left(\begin{array}{l} x_1^2 + x_2^2 - 7 \\ x_1^{-1} - x(2) \end{array} \right)
+\left(\begin{array}{l} x_1^2 + x_2^2 - 7 \\ x_1^{-1} - x_2 \end{array} \right)
 </latex>
-Use a contour plot of the norm of ''f'' over ''x(1), x(2)'' to find an
+Use a contour plot of the norm of $f$ over $x_1, x_2$ to find an
 initial guess for the search.
-**Problem 3:** Write a ''newtonsearchNd'' function that finds a zero of
+**Bonus (10 pts):** Write a ''newtonsearchNd'' function that finds a zero of
 an N-dimensional function ''f'' starting from the initial guess ''x''.
 Use this to find a zero of the nonlinear 3d function
@@ Line 45: / Line 45: @@
 \left(\begin{array}{l} 10(y-x) \\ x(28-z) - y \\ xy - 8/3 \; z \end{array} \right)
 </latex>
+Use the initial guess $[x,y,z] = [10, 10, 25]$.  Verify your answer by applying it to the 3d function. What do you expect to get?
+** Bonus (10 points): **
+Give a brief explanation for the Newton's Search. Include the answers to the following questions.
+** - ** Purpose: What is the Newton's method used for?
+** - ** Method: How does it do this? (How is it related to the Taylor Series? Can you explain the equations used in the code?)

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