§ Polynomial root finding using QR decomposition
- For a polynomial , build the companion matrix .
- Show that the characteristic polynomial of the companion matrix is indeed .
- Find eigenvalues of , which will be roots of , since the eigenvalues of a matrix are the roots of its characteristic polynomial .
- We use QR since it is numerically stable. The matrix discovered by QR is orthogonal, and hence does not disturb the covariance of the noise on matrix multiplication.