is a tridiagonal matrix (a square matrix with nonzero
entries along the main diagonal and the one immedi-
atel
y above it and the one belo
w it)
⎡⎤⎡⎤
⎢⎥⎢⎥
⎢⎥⎢
⎥
==
⎢⎥⎢⎥
⎢⎥⎢⎥
⎣⎦⎣⎦
11
22
and
nn
xd
xd
XD
xd
is known as a tridiagonal system. It can be solved by
LU decomposition method.
Howev
er, a computational method by Thomas
is given below.
Method
Step 1 Let a
1
=b
i
and compute the values of a
i
(i= 2, 3 …, n) using
1
1
; 2,3,,
ii
ii
i
ac
bina
a
−
−
=−=
(1.37)
Step 2 Let
1
1
1
d
b
b= and compute the values of
b
i
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