2015年3月5日 星期四

Difference Equations

Difference Equations

Recurrence relation


Fibonacci numbers


F_0 = 0

F_1 = 1

F_n = F_{n-1}+F_{n-2}




0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...


Linear homogeneous recurrence relations with constant coefficients

a_n = c_1a_{n-1} + c_2a_{n-2}+\cdots+c_da_{n-d},

the solution:
a_n = k_1 r_1^n + k_2 r_2^n + \cdots + k_d r_d^n,




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