• Use the Gauss-Seidel method to solve the following system until the percent relative error falls below e, = 5 % 10x, + 2x2 – x3 = 27 2х, — хз — 3х — бх, + 2х, — — 61.5 - X1 + X2 + 5x3 = – 21.5 | Same given, use Jacobi iteration
• Use the Gauss-Seidel method to solve the following system until the percent relative error falls below e, = 5 % 10x, + 2x2 – x3 = 27 2х, — хз — 3х — бх, + 2х, — — 61.5 - X1 + X2 + 5x3 = – 21.5 | Same given, use Jacobi iteration
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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Numerical Methods
Transcribed Image Text:• Use the Gauss-Seidel method to solve the
following system until the percent relative
error falls below e, = 5 %
10х, + 2х, — х; — 27
-3x, – 6x2 + 2x3 = – 61.5
X1 + X2 + 5x3 =
21.5
• Same given, use Jacobi iteration
![a. Use naive Gauss elimination to decompose the following
system according to the description
10x, + 2r2 - x3 = 27
-3x, - 6x2 + 2r3 = -61.5
X +xx + 5x3 = -21.5
%3D
Then, multiply the resulting [L] and [U] matrices to determine that
[A] is produced.
(b) Use LU decomposition to solve the system. Show all the steps
in the computation.
(c) Also solve the system for an alternative right-hand-side vector:
{B}T[12 18 6] .](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcaf9f5e5-3929-42b0-a5e3-6eb92bffbc89%2F7f84610e-b99d-41d1-bbe4-89c5610dfc13%2Fdkszef_processed.png&w=3840&q=75)
Transcribed Image Text:a. Use naive Gauss elimination to decompose the following
system according to the description
10x, + 2r2 - x3 = 27
-3x, - 6x2 + 2r3 = -61.5
X +xx + 5x3 = -21.5
%3D
Then, multiply the resulting [L] and [U] matrices to determine that
[A] is produced.
(b) Use LU decomposition to solve the system. Show all the steps
in the computation.
(c) Also solve the system for an alternative right-hand-side vector:
{B}T[12 18 6] .
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