Suppose we have a nxn linear system A = 6, but that the coefficient matrix A is not strictly diagonally dominant. Suppose that the system can not be re-arranged so that A is strictly diagonally dominant either. Suppose further that we apply the Gauss-Seidel method to this system with a very good initial approximation to the solution of the system, and that no mistakes are made. Then, the Gauss-Seidel method may generate a sequence of approximations that converges to the true solution of the system. True Ofalse Reset Selection

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.2: Norms And Distance Functions
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Suppose we have a nxn linear system Az = 6, but that the coefficient
matrix A is not strictly diagonally dominant.
Suppose that the system can not be re-arranged so that A is strictly
diagonally dominant either. Suppose further that we apply the Gauss-Seidel
method to this system with a very good initial approximation to the solution
of the system, and that no mistakes are made.
Then, the Gauss-Seidel method may generate a sequence of approximations that
converges to the true solution of the system.
True
False
Reset Selection
Transcribed Image Text:Suppose we have a nxn linear system Az = 6, but that the coefficient matrix A is not strictly diagonally dominant. Suppose that the system can not be re-arranged so that A is strictly diagonally dominant either. Suppose further that we apply the Gauss-Seidel method to this system with a very good initial approximation to the solution of the system, and that no mistakes are made. Then, the Gauss-Seidel method may generate a sequence of approximations that converges to the true solution of the system. True False Reset Selection
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