Math 222 MATLAB Supplementary lecture

Part 1: For loops and recurrence relations

Any formula which generates a sequence and gives

in terms of

is called a recurrence relation. Of course such a formula needs an initial value

. A very simple recurrence relation is

This define a sequence of values

N = 10;
n=0:N;                         % note that this starts from n=0
y = zeros(1,N+1);
y(1) = 0;
for j=1:N
    y(j+1) = y(j) + j;
end

We know, from first semester calculus (NJIT Math 111), that the exact solution to this recurrence is

yExact=n.*(n+1)/2; % Note the use of .* to multiply arrays!

We plot both of these on the same axis. Note the plotting syntax, including both the plots of both y and yExact, is not taught in the Onramp, but how it works should be obvious

plot(n,y,'o',n,yExact,'x')

xlabel('n');ylabel('y')

legend('y','yExact')