Faddeev–LeVerrier algorithm: Difference between revisions

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[[Image:Urbain Le Verrier.jpg|220px|thumb|right|[[Urbain Le Verrier]] (1811&ndash;1877)<br> The discoverer of [[Neptune]].]]

In mathematics ([[linear algebra]]), the '''Faddeev–LeVerrier algorithm''' is a [[Recurrence relation|recursive]] method to calculate the coefficients of the [[characteristic polynomial]] <math>p(\lambda)=\det (\lambda I_n - A)</math> of a square [[Matrix (mathematics)|matrix]], {{mvar|A}}, named after [[Dmitry Konstantinovich Faddeev]] and [[Urbain Le Verrier]]. Calculation of this polynomial yields the [[eigenvalue]]s of {{mvar|A}} as its roots; as a matrix polynomial in the matrix {{mvar|A}} itself, it vanishes by the fundamental [[Cayley–Hamilton theorem]]. Calculating determinants, however, is computationally cumbersome, whereas this efficient algorithm is computationally significantly more efficient (in [[NC (complexity)|NC complexity class]]).