... the coefficients aiare real, rather than complex, then the eigenvalues of A can befound using the routines balanc and hqr in§§11.5–11 .6 (see discussion there). Thismethod, implemented in the ... product involving the root and a reduced polynomial of degreeone less than the original, i.e., P (x)=(x−r)Q(x). Since the roots of Q areexactly the remaining roots of P, the effort of finding additional ... the desire to achieve full machineaccuracy, on the one hand, with the danger of iterating forever in the presence of roundoff error, on the other.#include <math.h>#include "complex.h"#include...