TP4

2015 −2016
n0
A
A L
U A =L U L 1
n= 3 L
U(`ij ) (uij )A aij
A n = 2 n= 3 n= 10 n= 1000
L U =A
A X =B B
L Y =B U X =Y L U 2
A
A[k, k] = 0 LU
A
k|aik|i≥k|ai0k|k
i0

A
L−1U−1
Adet(A) = det(L) det(U) = Qn
i=1 uii
A
n∈N∗(α1,· · · , αn)n
A= (αj−1
i)1≤i,j≤ndet(A) = Q1≤i<j≤n(αj−αi)
αi= 1/i n
Aixi=bii= 1,2,3
A1=
15 6 8 11
6 6 5 3
8 5 7 6
11 3 6 9
Ai=Ai
1i= 2,3bixi=t(1,1,1,1)
xi
A x =b
A=
2−2 0
ε−220
0−1 3
b x =t(1,1,1) ε≥0
x ε 0`32
ε= 10−10
ε