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Write Python code (or modify code in 4.4 ) to do the following: Input into a variable A the matrix ([4.1,2.8],[9.7,6.7]) . Input into a
Write Python code (or modify code in 4.4 ) to do the following:\ Input into a variable
A
the matrix
([4.1,2.8],[9.7,6.7])
.\ Input into a variable
b
the vector
(4.1,9.7)
.\ Use the LU method to solve the linear system
Av=b
. Denote the solution you find by
v1
.\ Input into a variable
db
the vector
(0.01,0)
.\ Use the LU method to solve the linear system
Av=b+db
. Denote the solution you find by
v2
.\ Evaluate, in any norm you choose,
||v1-v2|(|
|)/(
|
|)
|v1||
and show that this relative change of the solution is bound from above by the quantity
k(A)*||db|(|
|)/(
|
|)
|b||
, where
k(A)
is the matrix conditioning.
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