Given the tridiagonal matrix [1.45 0.087 0 0.37 1.0722 0.588 0 0 work out the values ,i=1,...,4 and u,,i=1,...,3 in the LU factorisation A=LU with L= 0 0.78 1.5468 0.6438 0 0.21 1.2718 0 01 0 0 0.78 13 0 0 0.21 14 Use the LU factorisation to solve the system Az = b with b= 0 11 0.37 0 0 12 -4.19572 -5.410072 -0.792684 5.0599 ,U = [1 ul 0 0 0 1 u2 0 0 0 1 u3 0 0 1
Given the tridiagonal matrix [1.45 0.087 0 0.37 1.0722 0.588 0 0 work out the values ,i=1,...,4 and u,,i=1,...,3 in the LU factorisation A=LU with L= 0 0.78 1.5468 0.6438 0 0.21 1.2718 0 01 0 0 0.78 13 0 0 0.21 14 Use the LU factorisation to solve the system Az = b with b= 0 11 0.37 0 0 12 -4.19572 -5.410072 -0.792684 5.0599 ,U = [1 ul 0 0 0 1 u2 0 0 0 1 u3 0 0 1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Given the tridiagonal matrix
1.45 0.087
0
0
0.37 1.0722 0.588 0
0
0
work out the values ,i=1,...,4 and u,,i = 1,...,3 in the LU
factorisation A = LU with
11
0 0
0.37
0 0
0
0.78 13 0
1
0 0 0.21 14
0 0 1
Use the LU factorisation to solve the system Az = =b with
L=
b=
0.78 1.5468 0.6438
0.21 1.2718
0
(c) 21
0
12
4.19572
-5.410072
-0.792684
5.0599
=
1, 11₂ =
U
for i=1,...,4
Use at least 6 decimal places for your calculations and specify
your final results to 2 decimal places.
(a) 4₁=
1,4₂ =
0.43=C
(b) u
2.
[1 ul
0
0 0
0
1 u2 0
u3
1. Ug =
x3 =
24
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