Systems of linear equations

Our Matlab function for naive Gaussian

elimination looks like this:

function x = naiv_gauss(A,b)

n = length(b) x = zeros(n,1)

for k=1:n-1 forward elimination

for i=k+1:n

xmult = A(i,k)/A(k,k)

for j=k+1:n

A(i,j) = A(i,j)-xmult*A(k,j)

end

b(i) = b(i)-xmult*b(k)

end

end

back substitution

x(n) = b(n)/A(n,n)

for i=n-1:-1:1

sum = b(i)

for j=i+1:n

sum = sum-A(i,j)*x(j)

end

x(i) = sum/A(i,i)

end-Systems of linear equations

Our Matlab function for naive Gaussian

elimination looks like this:

function x = naiv_gauss(A,b)

n = length(b)　x = zeros(n,1)

for k=1:n-1　 forward elimination

for i=k+1:n

xmult = A(i,k)/A(k,k)

for j=k+1:n

A(i,j) = A(i,j)-xmult*A(k,j)

end

b(i) = b(i)-xmult*b(k)

end

end

　back substitution

x(n) = b(n)/A(n,n)

for i=n-1:-1:1

sum = b(i)

for j=i+1:n

sum = sum-A(i,j)*x(j)

end

x(i) = sum/A(i,i)

end