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• 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

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 60EQ
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• 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
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] .
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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