Homework

Read Sections 1.3, 1.4 and 1.7, also section 1.2 but don't worry about the Taylor Series stuff.
Due Tuesday 2/3 :
- Section 1.3 Problem 1
- Write a paragraph or two about the matlab exercise and about playing with the base 2 calculator below.
Click for an opportunity to pick up brownie points:-) and possibly win recognition for our school (Henson)
Play with this base 2 calculator. Can you figure it out?
Due Thursday 2/12
- Section 2.6 2,4,7,10,11. For 7 and 10 compute the absolute and relative error if you solved the second system but should have solved the first. Comment.See my solution
Due Thursday 2/19 (if class is cancelled Tuesday 2/17 then due Tuesday 2/24)
- Section 7.1 all
- Section 7.2 1-6
- Sean found this Linear Agebra review helpful.
Due Tuesday 3/3
- Section 7.2 8, 10(A₅ is defined on the previous page), 11, 12, 13
During our class period on Tuesday or at someother time before Thursday morning: either on your own or in groups read the rest of 7.4 and figure out how to incorporate pivoting into your LU factorization routine. The textbook author uses a vector, indx to keep track of which rows were swapped so that at the end of the routine if indx(i)=j then the jth row from the initial matrix was used as the ith pivot so that when you want to solve Ax=b using the LU factorization, you first (in your forward solve routine or in advance of it) need to form a new b I will call it bp, he calls it x, where bp(i)=b(indx(i)). Implement this and test it. Then I want you to check what you are getting against the Matlab function : [L,U,P]=lu(A) Which returns L, U and a matrix P where P*b = bp from above. Figure out how to use the output from your routine to produce the L, U and P that the Matlab routine produces. Then please work through example 7.6 from section 7.5. Take a look at the rest of the section in preparation for our working through it together on Thursday.
Due Thursday 3/12
- Section 7.3 4,5,6,10,15
- Section 7.4 1,2,3,4,6,9
Due Tuesday 3/24
- Section 7.5 1-7 (that is 1,2,3,4,5,6,AND 7) (removed 5 and 6)
Due Tuesday 4/7 Note: I will not accept this assignment late since we will need to use this on Tuesday
- Section 8.1 1-5;7
Test 1 bonus is due Thursday 4/9
Due ~~Tuesday 4/21~~Thursday 4/23
- Section 8.2 1,4
- Section 8.3 Write a program to implement the basic power method, test it on a diagonal matrix with a strongly dominant eigenvalue. Then, once you are assured that it works in the test case, try it on the matrices from problem 1 in section 8.1. Some of these do NOT meet the hypotheses of the Thoerem. Note the number of iterations fro convergence if it occurs. COMMENT on what you find. Now repeat but use the Matlab hess command to reduce the matrices before sending them to your power method program. Comment!
Due Thursday 4/30
- Section 8.3 1, 6, 7
Due 5/7 which is also the day of our 2nd midterm
- Section 8.4 1, 2, write a routine that performs basic QR iteration. Test it on the matrices from problem 1 in section 8.1. Try it on some random symetric and non-symetric matrices. Try reducing to Hess form, vs not. Comment.
- Section 8.5 1, 2, 3 but ignore the Durand-Kerner question and the cost questions.