Solve the following system of
equations using LU factorization without partial
pivoting:
2x1 - 6x2 - x3 =
-38
-3x1 - x2 + x3 =
-34
-8x1 + x2 - 2x3 =
-20
Solve the following set of equations with LU factorization with
pivoting:
3x1 -2x2 + x3 = -10
2x1 + 6x2- 4x3 = 44
-8x1 -2x2 + 5x3 = -26
Please show all steps
Approximately how
many flops are needed to find the LU factorization of an n
x n matrix using Doolittle’s method? If a computer requires 1
second to find an LU factorization of a 500 x 500 matrix, what
would you estimate is the largest matrix that could be factored in
less than 1 hour?
Q: (LU decomposition) Find the LU decomposition of A = [-3 2 5
1; 12 -4 -20 -2; -6 0 15 1; -9 6 35 4]. You can use the compact
method which works within a single matrix or you can build L and U
separately. State L and U explicitly, and verify (in Matlab) that A
= L*U. Hint: Matlab's built-in lu function isn't useful, since it
pivots.
1.
Implement the recursive LU factorization algorithm in Python.
Use plenty of
comments to explain your code. While you are coding, it is
helpful to break up your code into sub-functions and test the
sub-functions as you go along.
Need a MATLAB code for LU factorization(both partial and
complete pivoting) of 10 random matrices of order 5x5.
Please do not comment like I don't have computer or I don't know
matlab. If you please answer otherwise you can skip.
Implement the recursive LU factorization algorithm in Python.
Use plenty of
comments to explain your code. While you are coding, it is
helpful to break up your code into sub-functions and test the
sub-functions as you go along.
Use LU decomposition to solve the following system of equations
(show your work). Do not use a pivoting strategy, and check your
results by using the matrix inverse to show that [A][A]-1= [I].
8x+ 2y−z=10
- 2x+4y+z=5
3x−y+ 6z=7
Explain how you can solve the following problems using the QR
factorization.
(a) Find the vector x that minimizes ||Ax − b1||^2 + ||Ax −
b2||^2 . The problem data are the m × n matrix A and two m-vectors
b1 and b2. The matrix A has linearly independent columns. If you
know several methods, give the most efficient one.
(b) Find x1 and x2 that minimize ||Ax1 − b1||^2 + ||Ax2 − b2||^2
. The problem data are the...