Question

Matlab Question. Please be detailed

Write a user-defined function that performs LU decomposition (using Gauss Elimination without partial pivoting) of a square matrix. Do not use built-in MATLAB functions lu( ), inv(), \, linsolve().

Matrices (in [A]*{x}={B} form)

A=[15 -3 -1; -3 15 -6; -4 -1 12]
B=[3800; 1200; 2350]

Given code lines:

function[L,U]=myLUFact_username(A)
[m,n]=size(A); %numbers of rows/comlumns of A
assert(m==n, 'A should be a square matrix');

Answer 1

`Hey,

Note: If you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

clc
clear all
close all
A=[15 -3 -1; -3 15 -6; -4 -1 12]
B=[3800; 1200; 2350]
[m,n]=size(A); %numbers of rows/comlumns of A

[L,U]=myLUFact_username(A)
% Now use a vector y to solve 'Ly=b'
y=zeros(m,1);
y(1)=B(1)/L(1,1);
for i=2:m
y(i)=-L(i,1)*y(1);
for k=2:i-1
y(i)=y(i)-L(i,k)*y(k);
y(i)=(B(i)+y(i))/L(i,i);
end
end
% Now we use this y to solve Ux = y
x=zeros(m,1);
x(1)=y(1)/U(1,1);
for i=2:m
x(i)=-U(i,1)*x(1);
for k=i:m
x(i)=x(i)-U(i,k)*x(k);
x(i)=(y(i)+x(i))/U(i,i);
end
end
x=x(:);
disp('Solution is');
disp(x);
function[L,U]=myLUFact_username(A)
[m,n]=size(A); %numbers of rows/comlumns of A
assert(m==n, 'A should be a square matrix');
if (m ~= n )
disp ( 'LR2 error: Matrix must be square' );
return;
end
% Part 2 : Decomposition of matrix into L and U
L=zeros(m,m);
U=zeros(m,m);
for i=1:m
% Finding L
for k=1:i-1
L(i,k)=A(i,k);
for j=1:k-1
L(i,k)= L(i,k)-L(i,j)*U(j,k);
end
L(i,k) = L(i,k)/U(k,k);
end
% Finding U
for k=i:m
U(i,k) = A(i,k);
for j=1:i-1
U(i,k)= U(i,k)-L(i,j)*U(j,k);
end
end
end
for i=1:m
L(i,i)=1;
end
  
end

Kindly revert for any queries

Thanks.