- #1
mathmari
Gold Member
MHB
- 5,049
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We have the linear system of equations with
First, I want to calculate the solution using the Gauss algorithm with complete pivoting, with accuracy and floating-point arithmetic with decimal places.
I have done the following:
The maximal element of the matrix is . We exchange the first and the last column and the first and last row (we make also the respective changes at the vector x and b)
So, we have the following:
So, we get the equations:
From the last equation we get .
From the second equationwe get .
From the first equation we get .
So we get the solution
The exact solution is (according to Wolfram) To check the accuracy of do we have to calculate the difference between the exact solution and the solution that we found? (Wondering)
I also have to calculate an estimate of the relative error using the condition number in respect of .
Do we have to use forthat the following inequality?
(Wondering)
First, I want to calculate the solution using the Gauss algorithm with complete pivoting, with accuracy
I have done the following:
The maximal element of the matrix is
So, we have the following:
So, we get the equations:
From the last equation we get
From the second equationwe get
From the first equation we get
So we get the solution
The exact solution is (according to Wolfram)
I also have to calculate an estimate of the relative error using the condition number in respect of
Do we have to use forthat the following inequality?
(Wondering)