COS 323, Fall 2010, Assignment 2
README.txt

Name:
NetID:


General Questions
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1. Give a concrete example of a function and starting upper and lower
bounds for which the false position method will require more iterations to
find the root than will bisection.  Justify your choice.  (You may, but are
not required to, implement bisection and false position to test your
hypothesis.)


[your answer here]


2. (Heath, exercise 6.9a)
Let f : R^n -> R be given by
  f(x) = 1/2 x^T A X - x^T b + c,
where A is an n x n symmetric positive definite matrix, b is an n-vector,
and c is a scalar.  Show that Newton's method for minimizing this function
converges in one iteration from any starting point x_0.


[your answer here]


3. (Heath, review question 2.80)
Suppose you have already solved the n x n linear system Ax=b by LU
factorization and back-substitution. What is the further cost (order of
magnitude will suffice) of solving a new system

a) With the same matrix but a different right-hand-side vector?
b) With the matrix changed by adding a matrix of rank one?
c) With the matrix changed completely?


[your answer here]



Programming assignment: The Pratt Truss Bridge
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Look at the pattern of compressive and tensile forces in the structure. 
Are the innermost diagonal members under compression or tension?  Which
beams have the greatest stresses for very tall bridges?  For very short
bridges?

Explain why the Calhoun Street Bridge in Trenton NJ shown above can use
cables for the diagonal members. 


[your answer here]


Based on your analysis, what can you say about when it's best to use different
values of n? (e.g., for fairly low bridges, is it better to use more or
fewer sections?)


[your answer here]


Brief description of your code, and any additional notes:


[your answer here]