Given the tridiagonal matrix 1.79 1.7363 0 0 0.2 1.254 0.2756 0 0 0.76 1.4076 0.3267 0.21 2.0567 0 0 work out the values 1,,i= 1,...,4 and u,,i = 1,...,3 in the LU factorisation A = LU with L 11 0 0.2 0 0 0 0.76 13 0 0 0 0.21 14 0 12 Use the LU factorisation to solve the system Az = b with 4.754777 -0.838472 2.011831 -7.300397 for i=1,...,4 (a) 4₁ (b) ₁ = (c) x₁ = Use at least 6 decimal places for your calculations and specify your final results to 2 decimal places. = ul 0 0 0 1 u2 0 0 0 1 u3 000 1 1 ₂ == 13 143 x3 = 00 x₁ ==
Given the tridiagonal matrix 1.79 1.7363 0 0 0.2 1.254 0.2756 0 0 0.76 1.4076 0.3267 0.21 2.0567 0 0 work out the values 1,,i= 1,...,4 and u,,i = 1,...,3 in the LU factorisation A = LU with L 11 0 0.2 0 0 0 0.76 13 0 0 0 0.21 14 0 12 Use the LU factorisation to solve the system Az = b with 4.754777 -0.838472 2.011831 -7.300397 for i=1,...,4 (a) 4₁ (b) ₁ = (c) x₁ = Use at least 6 decimal places for your calculations and specify your final results to 2 decimal places. = ul 0 0 0 1 u2 0 0 0 1 u3 000 1 1 ₂ == 13 143 x3 = 00 x₁ ==
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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Question
Jj.34.
Transcribed Image Text:Given the tridiagonal matrix
[1.79 1.7363 0
0
0.2 1.254 0.2756 0
0
0.76 1.4076 0.3267
0.21 2.0567
0
0
work out the values ,,i= 1,...,4 and u,,i= 1,...,3 in the LU factorisation
A=LU with
L =
b
11 0 0
0
0.2
12
0
0
0
0.76
13 0
0 0
0.21 14
Use the LU factorisation to solve the system Az = b with
for
4.754777
-0.838472
2.011831
-7.300397
i=1,...,4
Use at least 6 decimal places for your calculations and specify your
final results to 2 decimal places.
1, 43 = [
(a) 4₁
(b) ₁ =
(c) x₁ =
ul 0 0
0
1 u2 0
0 0 1 u3
00 0 1
½2
x₂ =
23
24 =
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