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Apply the Jacobi (iteration) method to solve the following system of linear equations, which has 4 equations and 4 unknowns (x1, x2, 23, C4): 3x1 – x2-4 = -2 -x1 + 4.x2 - x3 = 8 -x2+ 5x3- x4 = 4 -x1 – x3 + 3.4 = 10 In doing so, address the prompts below: 1. By hand, rewrite the given system of equations in standard form, [A]{x} = {b} (i.e. translate from list form to matrix form, with all unknowns collected in vector {x}) 2. Write your own MATLAB code to apply the Jacobi iteration method to this problem, using the following convergence criterion: E = 10-6 as the tolerance (a.k.a. error bound) (k+1) – x < e for i = 1, 2, 3, 4, with

Apply the Jacobi (iteration) method to solve the following system of linear equations, which has 4 equations and 4 unknowns (x1, x2, 23, C4): 3x1 – x2-4 = -2 -x1 + 4.x2 - x3 = 8 -x2+ 5x3- x4 = 4 -x1 – x3 + 3.4 = 10 In doing so, address the prompts below: 1. By hand, rewrite the given system of equations in standard form, [A]{x} = {b} (i.e. translate from list form to matrix form, with all unknowns collected in vector {x}) 2. Write your own MATLAB code to apply the Jacobi iteration method to this problem, using the following convergence criterion: E = 10-6 as the tolerance (a.k.a. error bound) (k+1) – x < e for i = 1, 2, 3, 4, with

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Apply the Jacobi (iteration) method to solve the following system of linear equations, which has 4 equations and 4 unknowns (x1, x2, 23, X4): 3x1 – x2 - x4 = -2 -x1 + 4.x2 – x3 = 8 -X2 + 5x3 - x4 = 4 -x1 – x3 + 3.x4 = 10 In doing so, address the prompts below: 1. By hand, rewrite the given system of equations in standard form, [A]{x} = {b} (i.e. translate from list form to matrix form, with all unknowns collected in vector {x}) 2. Write your own MATLAB code to apply the Jacobi iteration method to this problem, < e for i = 1,2, 3, 4, with (k+1) using the following convergence criterion: x e = 10-6 as the tolerance (a.k.a. error bound) 3. After your procedure has converged, report out (1) the final estimates of x1, x2, X3, x4 (or {x}) to at least 8 decimal places, (2) the number of iterations it took to converge, and (3) show that the error for every variable (x1, x2, x3, x4) is below the tolerance E
Transcribed Image Text:Apply the Jacobi (iteration) method to solve the following system of linear equations, which has 4 equations and 4 unknowns (x1, x2, 23, X4): 3x1 – x2 - x4 = -2 -x1 + 4.x2 – x3 = 8 -X2 + 5x3 - x4 = 4 -x1 – x3 + 3.x4 = 10 In doing so, address the prompts below: 1. By hand, rewrite the given system of equations in standard form, [A]{x} = {b} (i.e. translate from list form to matrix form, with all unknowns collected in vector {x}) 2. Write your own MATLAB code to apply the Jacobi iteration method to this problem, < e for i = 1,2, 3, 4, with (k+1) using the following convergence criterion: x e = 10-6 as the tolerance (a.k.a. error bound) 3. After your procedure has converged, report out (1) the final estimates of x1, x2, X3, x4 (or {x}) to at least 8 decimal places, (2) the number of iterations it took to converge, and (3) show that the error for every variable (x1, x2, x3, x4) is below the tolerance E
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