RECEQUN

RECEQUN - RECURRENCE EQUATION We solve recurrence equations...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: RECURRENCE EQUATION We solve recurrence equations often in analyzing complexity of algorithms, circuits, and such other cases. A homogeneous recurrence equation is written as: a t n + a 1 t n-1 + . . . . + a k t n-k = 0. Solution technique: Step 1 : Set up a corresponding Characteristic Equation: a x n + a 1 x (n-1) + . + a k x (n-k) = 0, x (n-k) [a x k + a 1 x (k-1) + +a k ] = 0, a x k + a 1 x k-1 + . . . . + a k = 0 [ for x =/= 0] Step 2 : Solve the characteristic equation as a polynomial equation. Say, the real roots are r 1 , r 2, . . . . , r k . Note, there are k solutions for k-th order polynomial equation. Step 3 : The general solution for the original recurrence equation is: t n = i=1 k c i r i n Step 4 : Using initial conditions (if available) solve for the coefficients in above equation in order to find the particular solution . Example 1 : t n 3t n-1 4t n-2 = 0, for n >= 2. {Initial condition: t0=0, t1=1} Characteristic equation: x n 3x (n-1) 4x (n-2)...
View Full Document

Page1 / 6

RECEQUN - RECURRENCE EQUATION We solve recurrence equations...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online