Computer Science 6676, Spring 1999                                         February 17, 1999
 

Assignment 3

Due Wednesday, March 3

 

  1. Chapter 4, problem 10. Include a brief proof or indication of why the accuracy is O(h^2).

    2.    Extra credit if you'd like an additional challenge: Chapter 4, problem 11.

  1. Chapter 5, problem 1.
  1. Chapter 5, problem 15.
  1. Chapter 5, problem 18.
  1. Chapter 5, problem 20.
  1. Produce the "evaluation graph" for the function 
      2. (x_1) / ((x_1)^2 + (x_2)^2)  +  (x_2) / ((x_1)^2) + (x_2)^2))

    as shown in class and in the notes from Nash and Sofer. Then show the sequence of steps that are used to (symbolically) form the gradient of f(x) from this graph using the reverse mode of automatic differentiation, as shown in class and in the notes from Nash and Sofer. (Note: you can either create the graph from the function as written, or first combine the two terms into one.)