Abraham Lincoln University Numerical Analysis Worksheet
Description
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Due date: Nov. 9th, 2022
1. Solve the linear system using Naive Gaussian elimination.
?
?? ? ? ?
1 2
3 1
x1
?1
?4 1
? ?x2 ? ? 2 ?
2
4
?
?? ? = ? ?
?2 1
1 3 ? ?x3 ? ? 1 ?
1 ?2 ?1 1
x4
?1
1
2
MATH135A HOMEWORK 4
3. (a) Solve the following system using naive Gaussian elimination with three-digits
(rounded) arithmetic and compare with the exact solution x1 = 1.00010… and x2 =
0.99989….
(
10?4 x1 + x2 = 1
x1 + x2
=2
(b) Repeat (a) after interchanging the order of two equations.
MATH135A HOMEWORK 4
3
4. Solve the following system using Gaussian elimination with scaled partial pivoting.
What is the scale vector? Show intermediate matrices and vectors.
?
?? ? ? ?
7
3 2 ?1
x1
? 5 3 2 ? ?x2 ? = ? 4 ?
?1
?1 1 ?3
x3
4
MATH135A HOMEWORK 4
5. Solve the following system of equation with n = 5 using Naive Gaussian. Calculate the
computational cost (Number of multiplication and additions).
?
?
= ?20
?4×1 ? x2
?xi?1 + 4xi ? xi+1 = 40, 2 ? i ? n ? 1
?
?
?xn?1 + 4xn
= ?20
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