Rewrite the linear system 6x + y + z = 1 x + 4y + z = 2 x + y + 5z = 0 in fixed-point form. Find bounds on x, y, and z such that fixed-point iteration is sure to converge for any initial guess (p0, q0, r0) that satisfies the boundary conditions.
Rewrite the linear system 6x + y + z = 1 x + 4y + z = 2 x + y + 5z = 0 in fixed-point form. Find bounds on x, y, and z such that fixed-point iteration is sure to converge for any initial guess (p0, q0, r0) that satisfies the boundary conditions.
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 23EQ
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Question
Rewrite the linear system
6x + y + z = 1
x + 4y + z = 2
x + y + 5z = 0
in fixed-point form. Find bounds on x, y, and z such that fixed-point iteration
is sure to converge for any initial guess (p0, q0, r0) that satisfies the boundary
conditions.
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