Numerical Methods • Use the Gauss-Seidel method to solve thefollowing system until the percent relativeerror falls below e, = 5 %10х, + 2х, — х; — 27-3x, – 6x2 + 2x3 = – 61.5X1 + X2 + 5x3 =21.5• Same given, use Jacobi iteration a. Use naive Gauss elimination to decompose the followingsystem according to the description10x, + 2r2 - x3 = 27-3x, - 6x2 + 2r3 = -61.5X +xx + 5x3 = -21.5%3DThen, multiply the resulting [L] and [U] matrices to determine that[A] is produced.(b) Use LU decomposition to solve the system. Show all the stepsin the computation.(c) Also solve the system for an alternative right-hand-side vector:{B}T[12 18 6] .

(Solving the first question) Solution: The percentage relative error is εs=0.005…

• 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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Question

Numerical Methods

• 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] .

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