Culegere de probleme de Analiz˘a numeric˘a
Culegere de probleme de Analiz˘a numeric˘a
Culegere de probleme de Analiz˘a numeric˘a
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66 Rezolvarea numerică a sistemelor algebrice liniare<br />
Γ11 = (−1) 1+1<br />
Γ13 = (−1) 1+3<br />
Γ22 = (−1) 1+2<br />
Γ31 = (−1) 3+1<br />
TGS = (D−L) −1 U =<br />
<br />
<br />
5 1 <br />
<br />
0 5 = 25, Γ12 = (−1) 1+2<br />
<br />
<br />
0 1 <br />
<br />
0 5 = 0<br />
<br />
<br />
0 5 <br />
<br />
0 0 = 0, Γ21 = (−1) 2+1<br />
<br />
<br />
1 1 <br />
<br />
0 5 = −5<br />
<br />
<br />
5 1 <br />
<br />
0 5 = 25, Γ23 = (−1) 2+3<br />
<br />
<br />
5 1 <br />
<br />
0 0 = 0<br />
<br />
<br />
1 1 <br />
<br />
5 1 = −5, Γ32 = (−1) 3+2<br />
<br />
<br />
5 1 <br />
<br />
0 1 = −5<br />
Γ33 = (−1) 3+3<br />
<br />
<br />
5 1 <br />
<br />
0 5 = 25<br />
E −1 ⎛<br />
1 0 0 5<br />
= ⎝ − 1 1 0 25 5<br />
− 1<br />
⎞<br />
⎠<br />
1 1 − 25 25 5<br />
⎛<br />
1 0 0 5<br />
⎝ − 1<br />
⎞⎛<br />
⎞ ⎛<br />
0 −1 −1 0 −<br />
1 0 ⎠⎝<br />
0 0 −1 ⎠<br />
25 5 = ⎝<br />
0 0 0<br />
1<br />
1 0 25<br />
− 1<br />
25<br />
− 1<br />
25<br />
1<br />
5<br />
TGSn = 2<br />
5<br />
<br />
2 k<br />
5<br />
3<br />
5<br />
· 7<br />
5<br />
< ε<br />
Problema 4.3.5 Arătat¸i că pentruA ∈ Mn,n(R)<br />
A2 = [ρ(A t A)] 1/2<br />
0 1<br />
25<br />
5 −1<br />
5<br />
− 4<br />
25<br />
2<br />
25<br />
⎞<br />
⎠
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