QR-decomposition

Various algorithms for computing the QR-decomposition of a matrix.

Description

1. Realized identifying of the intersection point of two parametric cubic splines through the QR-algorithm. (Task for 10)
2. Implemented QR-decomposition based on Gram-Schmidt orthogonalization. The stability of the new algorithm is compared with the method based on Householder matrices. (Task for 10)
3. Written a parallel algorithm for computing QR-decomposition. (Task for 10)

Also:

4. Realized the eigennumbers of a square matrix based on a QR-algorithm using the "qr" function from the "linalg" submodule of the Numpy library. In this case:

• the input matrix can have either complex-conjugate or multiple real roots;
• the input matrix has either only non-multiple real or complex eigenvalues, or real eigenvalues of multiplicity 2. (Task for 6-7)

5. Built QR-decomposition of the matrix from task for 6-7 using Householder reflection matrices. (Task for 8)