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
Metoda Gaussa |
Metoda Jackobiego |
Wyniki funkcji linsolve |
4.7222222 |
4.8124131 |
4.7222222 |
1.1111111 |
0.7503474 |
1.1111111 |
0.2777778 |
1.8110237 |
0.2777778 |
5.3874539 |
5.7468736 |
5.3874539 |
0.7468736 |
0.7468736 |
0.7468736 |
1.1764706 |
1.1764706 |
1.1764706 |
0.2941176 |
0.2941176 |
0.2941176 |
Wnioski
Wyniki metodą Gaussa i Jackobiego zgadzają się z funkcją linsolve.