4 x + z + t = 1; 4 y + t = 2; x + 4z = 3; Solution of the system x + y + 4t = 4 a) Check if it provides the diagonal efficiency. b) The largest eigenvalue of the iteration matrix is less than one, i.e. ρ (C) < Show that it is 1 (2D). c) Obtain the solution of the system by using Gauss-Seidel Method (2D)
4 x + z + t = 1; 4 y + t = 2; x + 4z = 3; Solution of the system x + y + 4t = 4 a) Check if it provides the diagonal efficiency. b) The largest eigenvalue of the iteration matrix is less than one, i.e. ρ (C) < Show that it is 1 (2D). c) Obtain the solution of the system by using Gauss-Seidel Method (2D)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.5: Iterative Methods For Solving Linear Systems
Problem 5EQ
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4 x + z + t = 1; 4 y + t = 2; x + 4z = 3; Solution of the system x + y + 4t = 4
a) Check if it provides the diagonal efficiency.
b) The largest eigenvalue of the iteration matrix is less than one, i.e. ρ (C) <
Show that it is 1 (2D).
c) Obtain the solution of the system by using Gauss-Seidel Method (2D)
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