工程数学 线性方程组直接解法数值试验

function x=gauss1(a,b) n=length(b); for k=1:n-1

for i=k+1:n

m(i,k)=a(i,k)/a(k,k); a(i,k)=0;

b(i)=b(i)-m(i,k)*b(k); for j=k+1:n

a(i,j)=a(i,j)-a(k,j)*m(i,k); end end end

x(n)=b(n)/a(n,n); for i=n-1:-1:1 s=0;

for j=i+1:n

s=s+a(i,j)*x(j); end

x(i)=(b(i)-s)/a(i,i); end x=x';

a=[2 3 4;3 5 2;4 3 30]; b=[6,5,32]' a(1,2)

a=[1 2 3;4 5 6;7 8 8];b=[6 15 23]; x=gauss1(a,b) x =

1

1 1 x =

NaN NaN NaN x =

-13 8 2

a=[2 -1 1;-1 -2 3;1 3 1] b=[ 4 5 6]’ x=gauss1(a,b) x=gauss1(a,b) x =

1.11111111111111 0.777777777777778 2.55555555555556 a=[12 -3 3;-18 3 1;1 1 1] b=[15 -15 6]’

x=gauss1(A,b)) m =

0 1.5 2 a =

2 3 4 0 0.5 -4 0 -3 22 b =

6 -4 20 m =

0 0 1.5 0 2 -6 a =

2 3 4 0 0.5 -4 0 0 -2 b =

6 -4 -4

x =

-13 8 2

function x=gauss4(a,b) a=[a,b];

n=length(b); for k=1:n-1 s=a(k,k);

p=k;

for i=k+1:n

if abs(s)

end

if p~=k

for j=k:n+1 t=a(k,j);

a(k,j)=a(p,j); a(p,j)=t; end end a,p

for i=k+1:n

m(i,k)=a(i,k)/a(k,k); a(i,k)=0;

for j=k+1:n+1

a(i,j)=a(i,j)-a(k,j)*m(i,k); end end end a

x(n)=a(n,n+1)/a(n,n); for i=n-1:-1:1 s=0;

for j=i+1:n

s=s+a(i,j)*x(j); end

x(i)=(a(i,n+1)-s)/a(i,i); end