It's a procedure to genearate the fibonacci numbers, here is the reference: http://sicp.org.ua/sicp/Exercise1-19
it's said that we can consider the procedure as "a <- bq + aq + ap and b <- bp + aq".My question is how the auther(or someone else) think out this good idea?Has it to be this form?
It's called the Fibonacci Q-Matrix, and the idea was "caught on like wildfire among Fibonacci enthusiasts. Numerous papers have appeared in Fibonacci Quarterly authored by Hoggatt and/or his students and other collaborators where the Q-matrix method became a central tool in the analysis of Fibonacci properties". You may refer to http://www.goldenmuseum.com/1505FibMatrix%5Fengl.html and http://mathworld.wolfram.com/FibonacciQ-Matrix.html.