Aim of the applet
Factorize a square matrix using the methods LU, QR and Choleski.
Solve the system of linear equations.
Input data
- The coefficient matrix, A
- The right side vector, b
The Calculate button will make factorizations of LU, QR and Choleski, if appropriate, and the solution of the linear system.
The user may specify the order of the matrix, as well as the number
de digit of the cells, from the block "Solving".
Output data
The applet will display in the corresponding block, the following information:
- Factorizations of pivoted LU, QR and Choleski.
- Solution vector of system AX=b
The applet also will notify the user if the system do not supports matrix factorization.
First steps
- With the 3x3 matrix A = (9 -2 0, -2 4 -1 0 -1 1) and the vector b = (5 1 -5 / 6), calculate the LU factorization, QR and Choleski of A and solves AX = b.
- Build a matrix A whose determinant is nonzero. Rename A = A * A ' and then make factorization the new A, what do you get?.
- With A defined by a_ij = min (i, j), 1 <= i, j <= n. b = (1.0 ,..)'. Solve for n = 5 by the three methods.
