10-TDMA.pdf

节选段落一：
Lange
Thomas Algorithm or
Tri-Diagonal Matrix Algorithm (TDMA)
Consider the system of algebraic equations:
[A][x] = [f ]
where
A =


a1 c1 0 · · ·
b2 a2 c2 0 · · ·
0 b3 a3 c3 0 · · ·
...
. . .
bn−1 an−1 cn−1
bn an


⇒ tri-diagonal matrix
A simplified version of the Gaussian Elimination


节选段落二：
is called Thomas Algorithm or
TDMA:
Forward Elimination
α1 = a1
g1 = f1
for i = 2 to n
βi =
bi
αi−1
αi = ai − βi ci−1
gi = fi − βi gi−1
end
Backward Substitution
xn =
gn
αn
for i = n− 1 to 1 step −1
xi =
(gi − ci xi+1)
αi
end