Description
Problem 1: Compute LU factorization of the matrix
-
3
0
−2
−2
= [
0
−1
3
−1]
−2
0
3
0
2
−2
1
2
Problem 2:
Solve the following system of equations by both LU factorization and QR factorization:
2 1− 3=−7
2 1 + 2 2 + 3 3 = 1
1+ 2+3 3=2
Problem 3:
Let be nonsingular × matrix. Show that has LU factorization = (no pivoting) with the diagonal terms of the matrix all nonzero if and only if for each 1 ≤ ≤ the upper left × submatrix 1: ,1: is nonsingular.
(Hint: Use induction argument).
Problem 4:
Compute the LU factorization with partial pivoting, (i.e., find P, L, U such that PA = LU ) for the following matrix
-
−1
−2
−1
−2
= [
3
−1
1
−1]
3
0
2
−1
0
1
−1
0
