Editing Recurrence relation (section)

===Stability of linear higher-order recurrences===
The linear recurrence of order <math>d</math>,

:<math>a_n = c_1a_{n-1} + c_2a_{n-2}+\cdots+c_da_{n-d},  </math>

has the [[Characteristic polynomial|characteristic equation]]

:<math>\lambda^d - c_1 \lambda^{d-1} - c_2 \lambda^{d-2} - \cdots - c_d \lambda^0 =0. </math>

The recurrence is [[Stability theory|stable]], meaning that the iterates converge asymptotically to a fixed value, if and only if the [[eigenvalues]] (i.e., the roots of the characteristic equation), whether real or complex, are all less than [[unity (mathematics)|unity]] in absolute value.