The matrix A has the decomposition A = LU, with L and U as below. 1 -4 1 2 0 0 00 00 4 4 0 1 2 10 0 0 -4 3 1 0 0 0 L = -3 0 0 1 0 4 4 1 U = 0 -1 0 2 0 12 2 3 0 6 1 -3 0 3/ Given Xo = (1.05, -5.93,-3.06, -5.92, 4.96) as an approximate solution to Ax=(3, -13, 45, -61, -201), calculate the residual ro. Now use Forward and Backward Substitution to obtain the error eo and correct the initial approximation.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
The matrix A has the decomposition A = LU, with L and U as below.
1
-4 1
2
0 0
00
00
4
4
0
1
2 10
0
0
-4 3 1
0 0 0
L
=
-3
0
0
1 0
4
4
1
U
=
0
-1 0 2
0 12
2 3
0 6 1
-3
0 3/
Given Xo = (1.05, -5.93,-3.06, -5.92, 4.96) as an approximate solution
to Ax=(3, -13, 45, -61, -201), calculate the residual ro.
Now use Forward and Backward Substitution to obtain the error eo and
correct the initial approximation.
Transcribed Image Text:The matrix A has the decomposition A = LU, with L and U as below. 1 -4 1 2 0 0 00 00 4 4 0 1 2 10 0 0 -4 3 1 0 0 0 L = -3 0 0 1 0 4 4 1 U = 0 -1 0 2 0 12 2 3 0 6 1 -3 0 3/ Given Xo = (1.05, -5.93,-3.06, -5.92, 4.96) as an approximate solution to Ax=(3, -13, 45, -61, -201), calculate the residual ro. Now use Forward and Backward Substitution to obtain the error eo and correct the initial approximation.
Expert Solution
steps

Step by step

Solved in 3 steps with 6 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,