ยง Polynomial root finding using QR decomposition
- For a polynomial p(x), build the companion matrix P(x).
- Show that the characteristic polynomial cp(P) of the companion matrix P(x) is indeed p(x).
- Find eigenvalues of P(x), which will be roots of p(x), since theeigenvalues of a matrix M are the roots of its characteristic polynomial cp(M).
- We use QR since it is numerically stable. The Q matrix discovered by QRis orthogonal, and hence does not disturb the covariance of the noiseon matrix multiplication.