*Computer Science 6676, Spring 1999
February 17, 1999
*

**Assignment 3**

Due Wednesday, March 3

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

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

- Chapter 5, problem 1.

- Chapter 5, problem 15.

- Chapter 5, problem 18.

- Chapter 5, problem 20.

- Produce the "evaluation graph" for the function

(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.)