Answer the given question with a proper explanation and step-by-step solution. Please provide solution in MATLAB.
Answer the given question with a proper explanation and step-by-step solution. Please provide solution in MATLAB.
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
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Question
Answer the given question with a proper explanation and step-by-step solution.
Please provide solution in MATLAB.
![In this problem, you have to implement the Gaussian elimination method with partial pivoting for solving the linear system Ax = b. For the algorithm, please see the lecture notes or the
textbook.
1 function [x, An, bn] =GEpivot (A,b)
2 % This program employs the Gaussian elimination method with partial
3 % pivoting to solve the linear system Ax=b.
4 %
5 % Input
6 % A: coefficient square matrix
7 %
b: right side column vector
%
9 % Output
10 % x: solution vector
11 % An, bn: coefficient matrix and right hand side vector after row operations
12
13 % check the order of the matrix and the size of the vector
14 [m,n]
size (A);
15 if m ~= n
end
16
17 end
18 m = length (b);
19 if m= n
20
21
22
23 % elimination step
24 for k= 1:n-1
25
26
27
28
29
30
31
error('The matrix is not square.')
=
error('The matrix and the vector do not match in size.')
% Pivoting: Find the maximal element in column k, starting from row k, then swap that row with row k:
for ik+1:n
end
if abs (A(i, k)) > abs (A(k,k))
% Swap rows k and i if the leading entry A(k,k) is smaller than A(i,k) in magnitude
% COMPLETE THE ROW SWAPPING. DO NOT FORGET THE RIGHT HAND SIDE AS WELL
end
end
32
33
34
35
36
37
38
39 end
40
41 % Backsubstitution: Solve the upper triangular linear system.
42 x zeros(n,1);
43 x(n) = b(n)/A(n,n);
44 for in-1:-1:1
% Row elimination.
for ik+1:n
% PERFORM ROW OPERATION: multiply row k by -A(i,k) and added to row i to eliminate A(i,k). Note that the leading entry has been normalized to one.
% Do not forget the right hand side vector
% COMPLETE THIS LINE to compute the solution
45
46 end
47
48 An = A; bn = b; % save the echelon form of the coefficient matrix and the corresponding right hand side vector.
49
Code to call your function >
1 A = [4 2 2; 1 -3 1; 2 2 3]; b = [1; 1; 1];
2 [x, An, bn] = GEpivot (A,b)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7cb6215-048b-47a5-b28f-7c86abf1a0e4%2Fcd67eabe-317b-4e4c-8d35-b3e138eb7a58%2Fmkui8mu_processed.png&w=3840&q=75)
Transcribed Image Text:In this problem, you have to implement the Gaussian elimination method with partial pivoting for solving the linear system Ax = b. For the algorithm, please see the lecture notes or the
textbook.
1 function [x, An, bn] =GEpivot (A,b)
2 % This program employs the Gaussian elimination method with partial
3 % pivoting to solve the linear system Ax=b.
4 %
5 % Input
6 % A: coefficient square matrix
7 %
b: right side column vector
%
9 % Output
10 % x: solution vector
11 % An, bn: coefficient matrix and right hand side vector after row operations
12
13 % check the order of the matrix and the size of the vector
14 [m,n]
size (A);
15 if m ~= n
end
16
17 end
18 m = length (b);
19 if m= n
20
21
22
23 % elimination step
24 for k= 1:n-1
25
26
27
28
29
30
31
error('The matrix is not square.')
=
error('The matrix and the vector do not match in size.')
% Pivoting: Find the maximal element in column k, starting from row k, then swap that row with row k:
for ik+1:n
end
if abs (A(i, k)) > abs (A(k,k))
% Swap rows k and i if the leading entry A(k,k) is smaller than A(i,k) in magnitude
% COMPLETE THE ROW SWAPPING. DO NOT FORGET THE RIGHT HAND SIDE AS WELL
end
end
32
33
34
35
36
37
38
39 end
40
41 % Backsubstitution: Solve the upper triangular linear system.
42 x zeros(n,1);
43 x(n) = b(n)/A(n,n);
44 for in-1:-1:1
% Row elimination.
for ik+1:n
% PERFORM ROW OPERATION: multiply row k by -A(i,k) and added to row i to eliminate A(i,k). Note that the leading entry has been normalized to one.
% Do not forget the right hand side vector
% COMPLETE THIS LINE to compute the solution
45
46 end
47
48 An = A; bn = b; % save the echelon form of the coefficient matrix and the corresponding right hand side vector.
49
Code to call your function >
1 A = [4 2 2; 1 -3 1; 2 2 3]; b = [1; 1; 1];
2 [x, An, bn] = GEpivot (A,b)
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