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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
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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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
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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