Matlab Demos in the Week-4 Lecture
Contents
A matix for which the growth factor reaches the maximum
For an order-n matrix, the growth factor of partial-pivot Gauss elimination can reach at most 2^(n-1). This is a theoretical maximum. For matrices in real applications this is hardly reachable.
n= 6; A= eye(n,n)-tril(ones(n,n), -1); A(:,n)= 1; A lugui(A, 'partial') % Let's see the growth factor from complete-pivot Gauss elimination. figure(2); lugui(A, 'complete')
A =
1 0 0 0 0 1
-1 1 0 0 0 1
-1 -1 1 0 0 1
-1 -1 -1 1 0 1
-1 -1 -1 -1 1 1
-1 -1 -1 -1 -1 1
Sparse matrix operations
n=20; S= spdiags([ones(n,1), -2*ones(n,1)], [-1, 2], n,n); figure(3); spy(S) S A= full(S); A whos
S =
(2,1) 1
(3,2) 1
(1,3) -2
(4,3) 1
(2,4) -2
(5,4) 1
(3,5) -2
(6,5) 1
(4,6) -2
(7,6) 1
(5,7) -2
(8,7) 1
(6,8) -2
(9,8) 1
(7,9) -2
(10,9) 1
(8,10) -2
(11,10) 1
(9,11) -2
(12,11) 1
(10,12) -2
(13,12) 1
(11,13) -2
(14,13) 1
(12,14) -2
(15,14) 1
(13,15) -2
(16,15) 1
(14,16) -2
(17,16) 1
(15,17) -2
(18,17) 1
(16,18) -2
(19,18) 1
(17,19) -2
(20,19) 1
(18,20) -2
A =
Columns 1 through 13
0 0 -2 0 0 0 0 0 0 0 0 0 0
1 0 0 -2 0 0 0 0 0 0 0 0 0
0 1 0 0 -2 0 0 0 0 0 0 0 0
0 0 1 0 0 -2 0 0 0 0 0 0 0
0 0 0 1 0 0 -2 0 0 0 0 0 0
0 0 0 0 1 0 0 -2 0 0 0 0 0
0 0 0 0 0 1 0 0 -2 0 0 0 0
0 0 0 0 0 0 1 0 0 -2 0 0 0
0 0 0 0 0 0 0 1 0 0 -2 0 0
0 0 0 0 0 0 0 0 1 0 0 -2 0
0 0 0 0 0 0 0 0 0 1 0 0 -2
0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
Columns 14 through 20
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
-2 0 0 0 0 0 0
0 -2 0 0 0 0 0
0 0 -2 0 0 0 0
1 0 0 -2 0 0 0
0 1 0 0 -2 0 0
0 0 1 0 0 -2 0
0 0 0 1 0 0 -2
0 0 0 0 1 0 0
0 0 0 0 0 1 0
Name Size Bytes Class Attributes
A 20x20 3200 double
S 20x20 528 double sparse
n 1x1 8 double
