legroots(c)
Return the roots (a.k.a. "zeros") of the polynomial
$$p(x) = \sum_i c[i] * L_i(x).$$The root estimates are obtained as the eigenvalues of the companion matrix, Roots far from the origin of the complex plane may have large errors due to the numerical instability of the series for such values. Roots with multiplicity greater than 1 will also show larger errors as the value of the series near such points is relatively insensitive to errors in the roots. Isolated roots near the origin can be improved by a few iterations of Newton's method.
The Legendre series basis polynomials aren't powers of x
so the results of this function may seem unintuitive.
1-D array of coefficients.
Array of the roots of the series. If all the roots are real, then :None:None:`out` is also real, otherwise it is complex.
Compute the roots of a Legendre series.
>>> import numpy.polynomial.legendre as legSee :
... leg.legroots((1, 2, 3, 4)) # 4L_3 + 3L_2 + 2L_1 + 1L_0, all real roots array([-0.85099543, -0.11407192, 0.51506735]) # may vary
The following pages refer to to this document either explicitly or contain code examples using this.
numpy.polynomial.hermite_e.hermeroots
numpy.polynomial.chebyshev.chebroots
numpy.polynomial.polynomial.polyroots
numpy.polynomial.hermite.hermroots
numpy.polynomial.laguerre.lagroots
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