linear vs non-linear recursion

Hi there,

I'm reading a book that considers two different methods to obtain a recursive formula for something. One method produces a non-linear recursion and the other produces a linear one. The authors comment that a difficulty with the first one is that it is non-linear - and this motivates the second method.

Why would a linear recursion be so much more preferable over a non-linear one? Is there a significant increase in computational load for the non-linear one? Or what?

Thanks