# cupyx.scipy.linalg.fiedler_companion¶

cupyx.scipy.linalg.fiedler_companion(a)

Returns a Fiedler companion matrix

Given a polynomial coefficient array a, this function forms a pentadiagonal matrix with a special structure whose eigenvalues coincides with the roots of a.

Parameters

a (cupy.ndarray) – 1-D array of polynomial coefficients in descending order with a nonzero leading coefficient. For N < 2, an empty array is returned.

Returns

Resulting companion matrix

Return type

cupy.ndarray

Notes

Similar to companion the leading coefficient should be nonzero. In the case the leading coefficient is not 1, other coefficients are rescaled before the array generation. To avoid numerical issues, it is best to provide a monic polynomial.