Use element-by-element Jacobi iteration to solve the system of equations Ax = b where 6 1-51 A-12 7 0-21 10 -1-2-31 2 H 10 and b = 3 2 You will be assessed on whether you've defined A and B correctly, whether the test for diagonal dominance is correct, whether one of the intermediate steps has been computed correctly, and whether the final step count and answer for x is correct. Make use of Matlab's help file to understand the functions being used. Script 1 2 %% Solving a matrix equation Ax=b using the Jacobi iterative technique. 3 % % The methods require A to be square and none of its main diagonal 4 %% elements can be zero. 5 6 A = ### 7 b = ### %% set b as a column vector 8 9 [# # #,N] = size(A); %%% M = number of rows, N = number of columns 10 if M~=N 11 error('A must be a square matrix') 12 end 13 14 %%% Test for diagonal dominance 15 %%% Check if the absolute value of the main diagonal elements is greater than 16 %%% the sum of the absolute value of the remaining terms in each row. 17 rowtest = abs(diag(A)) > sum(abs (A-diag(diag(A))),###); 18 index find (rowtest == ###); 19 if isempty (index) 20 21 22 23 end 24 disp("The matrix is not diagonally dominant.") disp("Take the results with caution.") pause(2) 25 % % The iterative process 26 x [0; 0; 0; 0; 0]; 27 xe = X 28 29 reldiff_tolerance = ###; 30 reldiff = 100; 31 k = 0; 32 % % The initial guess. %% setup another vector to store the new data %% set a tolerance of 10^-6 for the relative difference %% set reldiff arbitrarily high to begin %% to keep count of the number of iterations 33 fprintf('0, [%.6f, %.6f, %.6f, %.6f, %.6f]\n',x(1),x(2),x(3),x(4),x(5)); 34 while ### > ### x0(1) = (b(1)-A(1,2:M)*x(2:M))/A(1,1); %% all terms are to the right for j = 2 M-1 terms] = A(j,1:j-1)*x(1:j-1); %% terms to the left of the main diagonal termsr = ###; %% terms to the right of the main diagonal x0(j) (b(j)-termsl-termsr)/A(j,j); 35 36 37 38 39 40 end 41 42 43 k = k+1; 44 x = ###3 45 if k == 10 46 x10 = ###3 47 end x0(M) = (b(M)-A(M,1:M-1)*x(1:M-1))/A(M,M); % % all terms are to the left reldiff = abs(norm(x-x0))/norm(x0); %% increment the iteration count %% overwrite the old data with the new data %% automatically store the value of x when k=10 48 fprintf("%d, [%.6f, %.6f, %.6f, %.6f, %.6f]\n',k,x(1),x(2),x(3),x(4),x(5)); 49 end 50 xend ###; %% store the final value of x 51 kend ###;3 %% store the total number of iterations 52 53 Save CReset MATLAB Documentation ► Run Script ?
Use element-by-element Jacobi iteration to solve the system of equations Ax = b where 6 1-51 A-12 7 0-21 10 -1-2-31 2 H 10 and b = 3 2 You will be assessed on whether you've defined A and B correctly, whether the test for diagonal dominance is correct, whether one of the intermediate steps has been computed correctly, and whether the final step count and answer for x is correct. Make use of Matlab's help file to understand the functions being used. Script 1 2 %% Solving a matrix equation Ax=b using the Jacobi iterative technique. 3 % % The methods require A to be square and none of its main diagonal 4 %% elements can be zero. 5 6 A = ### 7 b = ### %% set b as a column vector 8 9 [# # #,N] = size(A); %%% M = number of rows, N = number of columns 10 if M~=N 11 error('A must be a square matrix') 12 end 13 14 %%% Test for diagonal dominance 15 %%% Check if the absolute value of the main diagonal elements is greater than 16 %%% the sum of the absolute value of the remaining terms in each row. 17 rowtest = abs(diag(A)) > sum(abs (A-diag(diag(A))),###); 18 index find (rowtest == ###); 19 if isempty (index) 20 21 22 23 end 24 disp("The matrix is not diagonally dominant.") disp("Take the results with caution.") pause(2) 25 % % The iterative process 26 x [0; 0; 0; 0; 0]; 27 xe = X 28 29 reldiff_tolerance = ###; 30 reldiff = 100; 31 k = 0; 32 % % The initial guess. %% setup another vector to store the new data %% set a tolerance of 10^-6 for the relative difference %% set reldiff arbitrarily high to begin %% to keep count of the number of iterations 33 fprintf('0, [%.6f, %.6f, %.6f, %.6f, %.6f]\n',x(1),x(2),x(3),x(4),x(5)); 34 while ### > ### x0(1) = (b(1)-A(1,2:M)*x(2:M))/A(1,1); %% all terms are to the right for j = 2 M-1 terms] = A(j,1:j-1)*x(1:j-1); %% terms to the left of the main diagonal termsr = ###; %% terms to the right of the main diagonal x0(j) (b(j)-termsl-termsr)/A(j,j); 35 36 37 38 39 40 end 41 42 43 k = k+1; 44 x = ###3 45 if k == 10 46 x10 = ###3 47 end x0(M) = (b(M)-A(M,1:M-1)*x(1:M-1))/A(M,M); % % all terms are to the left reldiff = abs(norm(x-x0))/norm(x0); %% increment the iteration count %% overwrite the old data with the new data %% automatically store the value of x when k=10 48 fprintf("%d, [%.6f, %.6f, %.6f, %.6f, %.6f]\n',k,x(1),x(2),x(3),x(4),x(5)); 49 end 50 xend ###; %% store the final value of x 51 kend ###;3 %% store the total number of iterations 52 53 Save CReset MATLAB Documentation ► Run Script ?
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
Related questions
Question
--- MATLAB work for Jacobi Iteration ---
--- Please answer the question in the attached image by replacing the ### with matlab script ---
--- Thank you in adavance ---
![Use element-by-element Jacobi iteration to solve the system of equations Ax = b where
6
1-51
A-12 7
0-21
10
-1-2-31
2
H
10
and b =
3
2
You will be assessed on whether you've defined A and B correctly, whether the test for diagonal dominance is correct, whether one of the intermediate steps has been computed
correctly, and whether the final step count and answer for x is correct.
Make use of Matlab's help file to understand the functions being used.
Script
1
2 %% Solving a matrix equation Ax=b using the Jacobi iterative technique.
3 % % The methods require A to be square and none of its main diagonal
4 %% elements can be zero.
5
6 A = ###
7 b = ###
%% set b as a column vector
8
9 [# # #,N] = size(A);
%%% M = number of rows, N = number of columns
10 if M~=N
11
error('A must be a square matrix')
12 end
13
14 %%% Test for diagonal dominance
15 %%% Check if the absolute value of the main diagonal elements is greater than
16 %%% the sum of the absolute value of the remaining terms in each row.
17 rowtest = abs(diag(A)) > sum(abs (A-diag(diag(A))),###);
18 index
find (rowtest == ###);
19 if isempty (index)
20
21
22
23 end
24
disp("The matrix is not diagonally dominant.")
disp("Take the results with caution.")
pause(2)
25 % % The iterative process
26 x [0; 0; 0; 0; 0];
27 xe = X
28
29 reldiff_tolerance = ###;
30 reldiff = 100;
31 k = 0;
32
% % The initial guess.
%% setup another vector to store the new data
%% set a tolerance of 10^-6 for the relative difference
%% set reldiff arbitrarily high to begin
%% to keep count of the number of iterations
33 fprintf('0, [%.6f, %.6f, %.6f, %.6f, %.6f]\n',x(1),x(2),x(3),x(4),x(5));
34 while ### > ###
x0(1) = (b(1)-A(1,2:M)*x(2:M))/A(1,1); %% all terms are to the right
for j = 2
M-1
terms] = A(j,1:j-1)*x(1:j-1); %% terms to the left of the main diagonal
termsr = ###; %% terms to the right of the main diagonal
x0(j)
(b(j)-termsl-termsr)/A(j,j);
35
36
37
38
39
40
end
41
42
43
k = k+1;
44
x = ###3
45
if k == 10
46
x10 = ###3
47
end
x0(M) = (b(M)-A(M,1:M-1)*x(1:M-1))/A(M,M); % % all terms are to the left
reldiff = abs(norm(x-x0))/norm(x0);
%% increment the iteration count
%% overwrite the old data with the new data
%% automatically store the value of x when k=10
48 fprintf("%d, [%.6f, %.6f, %.6f, %.6f, %.6f]\n',k,x(1),x(2),x(3),x(4),x(5));
49 end
50 xend ###;
%% store the final value of x
51 kend ###;3
%% store the total number of iterations
52
53
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CReset
MATLAB Documentation
► Run Script
?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2476f823-c3c8-40b1-886d-66e8e64f59f9%2F1271f120-8aa6-4aa9-92f2-a16fed2eae1c%2Fsfjuksa_processed.png&w=3840&q=75)
Transcribed Image Text:Use element-by-element Jacobi iteration to solve the system of equations Ax = b where
6
1-51
A-12 7
0-21
10
-1-2-31
2
H
10
and b =
3
2
You will be assessed on whether you've defined A and B correctly, whether the test for diagonal dominance is correct, whether one of the intermediate steps has been computed
correctly, and whether the final step count and answer for x is correct.
Make use of Matlab's help file to understand the functions being used.
Script
1
2 %% Solving a matrix equation Ax=b using the Jacobi iterative technique.
3 % % The methods require A to be square and none of its main diagonal
4 %% elements can be zero.
5
6 A = ###
7 b = ###
%% set b as a column vector
8
9 [# # #,N] = size(A);
%%% M = number of rows, N = number of columns
10 if M~=N
11
error('A must be a square matrix')
12 end
13
14 %%% Test for diagonal dominance
15 %%% Check if the absolute value of the main diagonal elements is greater than
16 %%% the sum of the absolute value of the remaining terms in each row.
17 rowtest = abs(diag(A)) > sum(abs (A-diag(diag(A))),###);
18 index
find (rowtest == ###);
19 if isempty (index)
20
21
22
23 end
24
disp("The matrix is not diagonally dominant.")
disp("Take the results with caution.")
pause(2)
25 % % The iterative process
26 x [0; 0; 0; 0; 0];
27 xe = X
28
29 reldiff_tolerance = ###;
30 reldiff = 100;
31 k = 0;
32
% % The initial guess.
%% setup another vector to store the new data
%% set a tolerance of 10^-6 for the relative difference
%% set reldiff arbitrarily high to begin
%% to keep count of the number of iterations
33 fprintf('0, [%.6f, %.6f, %.6f, %.6f, %.6f]\n',x(1),x(2),x(3),x(4),x(5));
34 while ### > ###
x0(1) = (b(1)-A(1,2:M)*x(2:M))/A(1,1); %% all terms are to the right
for j = 2
M-1
terms] = A(j,1:j-1)*x(1:j-1); %% terms to the left of the main diagonal
termsr = ###; %% terms to the right of the main diagonal
x0(j)
(b(j)-termsl-termsr)/A(j,j);
35
36
37
38
39
40
end
41
42
43
k = k+1;
44
x = ###3
45
if k == 10
46
x10 = ###3
47
end
x0(M) = (b(M)-A(M,1:M-1)*x(1:M-1))/A(M,M); % % all terms are to the left
reldiff = abs(norm(x-x0))/norm(x0);
%% increment the iteration count
%% overwrite the old data with the new data
%% automatically store the value of x when k=10
48 fprintf("%d, [%.6f, %.6f, %.6f, %.6f, %.6f]\n',k,x(1),x(2),x(3),x(4),x(5));
49 end
50 xend ###;
%% store the final value of x
51 kend ###;3
%% store the total number of iterations
52
53
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CReset
MATLAB Documentation
► Run Script
?
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