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Mathematical Methods by Pearson
book

Mathematical Methods by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
437 pages
17h 41m
English
Pearson India
Content preview from Mathematical Methods by Pearson
Matrices and Linear Systems of Equations 1-41
AX = D (1.36)
where
11
222
33 3
111
00
0
000
000
000 0
nnn
nn
bc
abc
ab c
A
abc
ab
−−−
⎡⎤
⎢⎥
⎢⎥
⎢⎥
=
⎢⎥
⎢⎥
⎢⎥
⎢⎥
⎢⎥
⎣⎦



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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Publisher Resources

ISBN: 9781299446557Publisher Website