Math 344 - Numerical Methods II - Homework Assignments

Assignment 1 | Assignment 2 | Assignment 3 | Assignment 4 | Assignment 5
Date/Section Assignment / Due Date
Jan 15/(4.1.1) Assignment 1 - Turn in on Jan. 20
 
  • Page 201 (handout): #2, #3, #8(a)(b)
  • *Describe the following regions:
    (1) {x in R2; ||x||2 <= 1} and
    (2) {x in R2; ||x||infinity <= 1}.
Problems with * will be presented in class by assigned presenter.
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Jan 16/(4.1.2) Assignment 2 - Turn in on Jan. 26
  Page 211 (handout): #4(a), #5(a)(b) (eigenvalues only), #6(a)(b) (eigenvalues only), #7(a)(b), #8(a)(b), *#9, *#11, *#12, #19(a)(c)
Problems with * will be presented in class by assigned presenter.
Note: MatLab Handout 1 discusses how to compute eigenvalues and eigenvectors of a given matrix and how to find the number of linearly independent eigenvectors using MatLab.
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Jan 26/(4.2.1)&(4.2.2) Assignment 3 - Turn in on Jan. 29
  Page 220 (handout): #3, #5(a), #6
Page 223 (handout): #2(b), compute the condition number of matrix A in infinity norm in terms of epsilon first and then evaluate the condition numbers for epsilon=0.001 and epsilon=0.00001 where 
   A=[1         2]
     [1+epsilon 2].
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Jan 29/(4.3.1)&(4.3.2) Assignment 4 - Turn in on Feb. 2
  Page 232 (handout): #5, #6, #7
Page 240 (handout): #5, #6, #7
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Feb 10/(4.3.3) Assignment 5 - Turn in on Feb. 16
 
  1. Page 245 (handout): #1(a), #2(d) - for these problems, compute rho(Tomega) only for the given omega
    #6, #7
    Page 548: #4, #11
  2. Let lambda1,...,lambdan be eigenvalues of an nxn matrix A where
    |lambda1| > |lambda2| >= ... >= |lambdan|.
    Find all eigenvalues of matrix B=A-lambda1 I
    (relating to lambdai's).
  3. Let A=[3 2 1;2 2 -1;1 -1 5].
    • Use the Gerschgorin Circle Theorem to find the interval on the real line which contains all eigenvalues of A.
    • From the obtained information, can we conclude that A is nonsingular, or A is positive definite?
    • Compute all eigenvalues of A (by any way you like - calculator, MatLab, hand, ...). Check if they are in the region obtained previously.
    • Is A nonsingular? Is A positive definite?
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