Thread: Error Formula

For the recursive algorithm p0=1, p1=1/3, pn=(10/3)(pn-1 - pn-2) for n >1 let the error be denoted by p'=pn+en for initial error e0, and assume the error has the form

p'0=p0+e0
p'1=p1+3e0
p'n=(10/3)(p'n-1 - p'n-2) for n>1

so that e1=3e0
Find an equation for en in terms of e0, n, and a constant.

Originally Posted by veronicak5678

For the recursive algorithm p0=1, p1=1/3, pn=(10/3)(pn-1 - pn-2) for n >1 let the error be denoted by p'=pn+en for initial error e0, and assume the error has the form

p'0=p0+e0
p'1=p1+3e0
p'n=(10/3)(p'n-1 - p'n-2) for n>1

so that e1=3e0
Find an equation for en in terms of e0, n, and a constant.

is a linear difference equation, so suppose for some real number , then find the characteristic equation and solve for . Form the general solution as a linear combination of the two solutions you will have found and fit to the initial conditions.

CB

Could you please explain how to find the characteristic equation?

Originally Posted by veronicak5678

Could you please explain how to find the characteristic equation?

You make the substitution in the difference equarion to get:



Now divide through by to get:



which is a quadratic in which rearranges to:



which is the charateristic equation which you solve for .

CB

I see. Thanks!