Gauss


Metoda Gaussa

-->A=[40,10,0,0,0,0,0;-10,40,10,0,0,0,0;0,-10,40,-10,-10,0,0;0,0,-10,40,0,-10,0;0,0,-10,0,40,-10,0;0,0,0,-10,10,40,10;0,0,0,0,0,-10,40]

A =

40. 10. 0. 0. 0. 0. 0.

- 10. 40. 10. 0. 0. 0. 0.

0. - 10. 40. - 10. - 10. 0. 0.

0. 0. - 10. 40. 0. - 10. 0.

0. 0. - 10. 0. 40. - 10. 0.

0. 0. 0. - 10. 10. 40. 10.

0. 0. 0. 0. 0. - 10. 40.

-->b=[200;0;0;200;0;0;0]

b =

200.

0.

0.

200.

0.

0.

0.

-->Ab=[A b]

Ab =

40. 10. 0. 0. 0. 0. 0. 200.

- 10. 40. 10. 0. 0. 0. 0. 0.

0. - 10. 40. - 10. - 10. 0. 0. 0.

0. 0. - 10. 40. 0. - 10. 0. 200.

0. 0. - 10. 0. 40. - 10. 0. 0.

0. 0. 0. - 10. 10. 40. 10. 0.

0. 0. 0. 0. 0. - 10. 40. 0.

-->L12 = Ab(2,1)/Ab(1,1)

L12 =

- 0.25

-->Ab(2,:)=Ab(2,:)-L12*Ab(1,:)

Ab =

40. 10. 0. 0. 0. 0. 0. 200.

0. 42.5 10. 0. 0. 0. 0. 50.

0. - 10. 40. - 10. - 10. 0. 0. 0.

0. 0. - 10. 40. 0. - 10. 0. 200.

0. 0. - 10. 0. 40. - 10. 0. 0.

0. 0. 0. - 10. 10. 40. 10. 0.

0. 0. 0. 0. 0. - 10. 40. 0.

-->L23=Ab(3,2)/Ab(2,2)

L23 =

- 0.2352941

-->Ab(3,2:$)=Ab(3,2:$)-L23*Ab(2,2:$)

Ab =

40. 10. 0. 0. 0. 0. 0. 200.

0. 42.5 10. 0. 0. 0. 0. 50.

0. 0. 42.352941 - 10. - 10. 0. 0. 11.764706

0. 0. - 10. 40. 0. - 10. 0. 200.

0. 0. - 10. 0. 40. - 10. 0. 0.

0. 0. 0. - 10. 10. 40. 10. 0.

0. 0. 0. 0. 0. - 10. 40. 0.

-->L34=Ab(4,3)/Ab(3,3)

L34 =

- 0.2361111

-->Ab(4,3:$)=Ab(4,3:$)-L34*Ab(3,3:$)

Ab =

40. 10. 0. 0. 0. 0. 0. 200.

0. 42.5 10. 0. 0. 0. 0. 50.

0. 0. 42.352941 - 10. - 10. 0. 0. 11.764706

0. 0. 0. 37.638889 - 2.3611111 - 10. 0. 202.77778

0. 0. - 10. 0. 40. - 10. 0. 0.

0. 0. 0. - 10. 10. 40. 10. 0.

0. 0. 0. 0. 0. - 10. 40. 0.

-->L45=Ab(5,3)/Ab(4,4)

L45 =

- 0.2656827

-->L45=Ab(5,3)/Ab(3,3)

L45 =

- 0.2361111

-->Ab(5,3:$)=Ab(5,3:$)-L45*Ab(3,3:$)

Ab =

40. 10. 0. 0. 0. 0. 0. 200.

0. 42.5 10. 0. 0. 0. 0. 50.

0. 0. 42.352941 - 10. - 10. 0. 0. 11.764706

0. 0. 0. 37.638889 - 2.3611111 - 10. 0. 202.77778

0. 0. 0. - 2.3611111 37.638889 - 10. 0. 2.7777778

0. 0. 0. - 10. 10. 40. 10. 0.

0. 0. 0. 0. 0. - 10. 40. 0.

-->L56=Ab(6,4)/Ab(4,4)

L56 =

- 0.2656827

-->Ab(6,4:$)=Ab(6,4:$)-L56*Ab(4,4:$)

Ab =

40. 10. 0. 0. 0. 0. 0. 200.

0. 42.5 10. 0. 0. 0. 0. 50.

0. 0. 42.352941 - 10. - 10. 0. 0. 11.764706

0. 0. 0. 37.638889 - 2.3611111 - 10. 0. 202.77778

0. 0. 0. - 2.3611111 37.638889 - 10. 0. 2.7777778

0. 0. 0. 0. 9.3726937 37.343173 10. 53.874539

0. 0. 0. 0. 0. - 10. 40. 0.

-->L45=Ab(5,4)/Ab(4,4)

L45 =

- 0.0627306

-->Ab(5,4:$)=Ab(5,4:$)-L45*Ab(4,4:$)

Ab =

40. 10. 0. 0. 0. 0. 0. 200.

0. 42.5 10. 0. 0. 0. 0. 50.

0. 0. 42.352941 - 10. - 10. 0. 0. 11.764706

0. 0. 0. 37.638889 - 2.3611111 - 10. 0. 202.77778

0. 0. 0. 0. 37.490775 - 10.627306 0. 15.498155

0. 0. 0. 0. 9.3726937 37.343173 10. 53.874539

0. 0. 0. 0. 0. - 10. 40. 0.

-->L56=Ab(6,5)/Ab(5,5)

L56 =

0.25

-->Ab(6,5:$)=Ab(6,5:$)-L56*Ab(5,5:$)

Ab =

40. 10. 0. 0. 0. 0. 0. 200.

0. 42.5 10. 0. 0. 0. 0. 50.

0. 0. 42.352941 - 10. - 10. 0. 0. 11.764706

0. 0. 0. 37.638889 - 2.3611111 - 10. 0. 202.77778

0. 0. 0. 0. 37.490775 - 10.627306 0. 15.498155

0. 0. 0. 0. 0. 40. 10. 50.

0. 0. 0. 0. 0. - 10. 40. 0.

-->L67=Ab(7,6)/Ab(6,6)

L67 =

- 0.25

-->Ab(7,6:$)=Ab(7,6:$)-L67*Ab(6,6:$)

Ab =

40. 10. 0. 0. 0. 0. 0. 200.

0. 42.5 10. 0. 0. 0. 0. 50.

0. 0. 42.352941 - 10. - 10. 0. 0. 11.764706

0. 0. 0. 37.638889 - 2.3611111 - 10. 0. 202.77778

0. 0. 0. 0. 37.490775 - 10.627306 0. 15.498155

0. 0. 0. 0. 0. 40. 10. 50.

0. 0. 0. 0. 0. 0. 42.5 12.5

-->X(7)=Ab(7,8)/Ab(7,7)

X =

0.

0.

0.

0.

0.

0.

0.2941176

-->X(6)=(Ab(6,8)-Ab(6,7)*X(7))/Ab(6,7)

X =

0.

0.

0.

0.

0.

4.7058824

0.2941176

-->X(6)=(Ab(6,8)-Ab(6,7)*X(7))/Ab(6,6)

X =

0.

0.

0.

0.

0.

1.1764706

0.2941176

-->X(5)=(Ab(5,8)-Ab(5,6)*X(6))/Ab(5,5)

X =

0.

0.

0.

0.

0.7468736

1.1764706

0.2941176

-->X(4)=(Ab(4,8)-Ab(6,4)*X(6)-Ab(5,4)*X(5))/Ab(4,4)

X =

0.

0.

0.

5.3874539

0.7468736

1.1764706

0.2941176

-->X(3)=(Ab(3,8)-Ab(6,3)*X(5)-Ab(5,3)*X(4))/Ab(3,3)

X =

0.

0.

0.2777778

5.3874539

0.7468736

1.1764706

0.2941176

-->X(2)=(Ab(2,8)-Ab(2,3)*X(3))/Ab(2,2)

X =

0.

1.1111111

0.2777778

5.3874539

0.7468736

1.1764706

0.2941176

-->X(1)=(Ab(1,8)-Ab(1,2)*X(2))/Ab(1,1)

X =

4.7222222

1.1111111

0.2777778

5.3874539

0.7468736

1.1764706

0.2941176

Metoda Jackobiego

-->A=[40,10,0,0,0,0,0;-10,40,10,0,0,0,0;0,-10,40,-10,-10,0,0;0,0,-10,40,0,-10,0;0,0,-10,0,40,-10,0;0,0,0,-10,10,40,10;0,0,0,0,0,-10,40]

A =

40. 10. 0. 0. 0. 0. 0.

- 10. 40. 10. 0. 0. 0. 0.

0. - 10. 40. - 10. - 10. 0. 0.

0. 0. - 10. 40. 0. - 10. 0.

0. 0. - 10. 0. 40. - 10. 0.

0. 0. 0. - 10. 10. 40. 10.

0. 0. 0. 0. 0. - 10. 40.

-->b=[200;0;0;200;0;0;0]

b =

200.

0.

0.

200.

0.

0.

0.

-->L=tril(A, -1)

L =

0. 0. 0. 0. 0. 0. 0.

- 10. 0. 0. 0. 0. 0. 0.

0. - 10. 0. 0. 0. 0. 0.

0. 0. - 10. 0. 0. 0. 0.

0. 0. - 10. 0. 0. 0. 0.

0. 0. 0. - 10. 10. 0. 0.

0. 0. 0. 0. 0. - 10. 0.

-->D=diag(diag(A))

D =

40. 0. 0. 0. 0. 0. 0.

0. 40. 0. 0. 0. 0. 0.

0. 0. 40. 0. 0. 0. 0.

0. 0. 0. 40. 0. 0. 0.

0. 0. 0. 0. 40. 0. 0.

0. 0. 0. 0. 0. 40. 0.

0. 0. 0. 0. 0. 0. 40.

-->U=triu(A,1)

U =

0. 10. 0. 0. 0. 0. 0.

0. 0. 10. 0. 0. 0. 0.

0. 0. 0. - 10. - 10. 0. 0.

0. 0. 0. 0. 0. - 10. 0.

0. 0. 0. 0. 0. - 10. 0.

0. 0. 0. 0. 0. 0. 10.

0. 0. 0. 0. 0. 0. 0.

-->Dinv=inv(D)

Dinv =

0.025 0. 0. 0. 0. 0. 0.

0. 0.025 0. 0. 0. 0. 0.

0. 0. 0.025 0. 0. 0. 0.

0. 0. 0. 0.025 0. 0. 0.

0. 0. 0. 0. 0.025 0. 0.

0. 0. 0. 0. 0. 0.025 0.

0. 0. 0. 0. 0. 0. 0.025

column 1 to 13

200. 5. - 7.5 7.8125 6.328125 5.1953125 4.7167969 4.8120117 4.8242188 4.8168945 4.8116684 4.8123169 4.8125052

0. 50. - 11.25 - 5.3125 - 0.78125 1.1328125 0.7519531 0.703125 0.7324219 0.7533264 0.7507324 0.7499790 0.7501841

0. 50. 13.75 10.9375 1.796875 2.1875 1.9042969 1.8823242 1.8109131 1.8139648 1.8117523 1.8115807 1.8110228

200. 5. 30. 8.75 7.265625 5.7421875 5.8886719 5.7702637 5.7617188 5.7468414 5.7477951 5.747056 5.7470012

0. 0. 25. 3.75 2.265625 0.7421875 0.8886719 0.7702637 0.7617188 0.7468414 0.7477951 0.7470560 0.7470012

0. 50. 1.25 - 1.875 1.171875 1.3671875 1.1767578 1.1645508 1.1764526 1.1772156 1.1764717 1.176424 1.1764705

0. 0. 12.5 0.3125 - 0.46875 0.2929688 0.3417969 0.2941895 0.2911377 0.2941132 0.2943039 0.2941179 0.2941060

column 14 to 20

4.812454 4.8124073 4.812412 4.8124139 4.8124135 4.8124131 4.8124131

0.7503706 0.7503518 0.7503445 0.7503460 0.7503476 0.7503474 0.7503474

1.8110466 1.8110293 1.811028 1.8110236 1.8110238 1.8110237 1.8110237

5.7468733 5.74688 5.746875 5.7468746 5.7468736 5.7468736 5.7468736

0.7468733 0.7468800 0.7468750 0.7468746 0.7468736 0.7468736 0.7468736

1.1764735 1.1764706 1.1764704 1.1764706 1.1764706 1.1764706 1.1764706

0.2941176 0.2941184 0.2941176 0.2941176 0.2941176 0.2941176 0.2941176

-->Xtest=linsolve(A,-b)

4.7222222

1.1111111

0.2777778

5.3874539

0.7468736

1.1764706

0.2941176