Graphics Programs Reference
In-Depth Information
The edges of the square plate arekept at the temperatures shown. Assuming
steady-state heatconduction, the differentialequationgoverning the temperature
T in the interioris
2 T
+
2 T
=
0
x 2
y 2
If thisequationis approximated by finite differences using the mesh shown,
weobtain the following algebraicequationsfor temperatures at the mesh
points:
4
1
0
1
00000
T 1
T 2
T 3
T 4
T 5
T 6
T 7
T 8
T 9
0
0
100
0
0
100
200
200
300
1
4
1
0
1
0000
0
1
4001
000
1
00
4
1
0
1
00
0
1
0
1
4
1
0
1
0
=−
001
0
1
4001
0001
00
4
1
0
00001
0
1
4
1
000001
0
1
4
Solve these equations with the conjugate gradient method.
MATLAB Functions
b ,obtainedbyGauss elimination. If the equa-
tions areoverdetermined ( A has more rowsthan columns), the least-squares
solutioniscomputed.
[L,U] = lu(A) Doolittle's decomposition A
\
b returns the solution x of Ax
=
x=A
=
LU . Onreturn, U is an upper trian-
gular matrix and L contains arow-wise permutation of the lower triangular
matrix.
[M,U,P] = lu(A) returns the same U as above, but now M is a lower triangularmatrix
and P is the permutationmatrix so that M = P*L . Note thathere P*A = M*U .
L = chol(A) Choleski's decomposition A
LL T .
B = inv(A) returns B as the inverse of A (the methodusedis not specified).
n = norm(A,1) returns the norm n
=
max j i |
=
A i j |
(largest sum of elements in a
column of A ).
c = cond(A) returns the condition number of the matrix A .
Search WWH ::

Custom Search