MTH3051 Introduction to Computational Mathematics - User Web ...

School of Mathematical Sciences
Monash University
looping as each term is calculated. Here is the final code
% --- set initial values ----------------------------------------
k = 0;
x = 1.23;
sum = 1;
term = 1;
k_max = 100;
looping = true;
x_square = x*x;
% --- compute successive terms in the series --------------------
while looping
end
k = k + 1;
term = - term*x_square/( (2*k)*(2*k-1) );
sum = sum + term;
if ( abs(term) < 0.00001 )
looping = false;
end
if ( k > k_max )
looping = false;
end
answer = sum;
There are quite a few changes introduced in the above code. We have replaced the for
loop with a while loop. Thus we have also been forced to explicitly increment k (i.e.
the line k = k + 1) and to limit the number of terms (hence the new variable k max).
Though the above code is longer than the previous version it is (in my opinion) easier to
read and better conveys what we are actually doing (i.e. looping until we reach a given
accuracy).
Compare this code with that given for sin(x) at the start of these notes. You will see
that they are similar but they do have important differences (as they should, after all
sin(x) and cos(x) are different functions). Note in particular the way term is calculated,
and the initial values for k and sum. If you have any doubts that they are correct one
way to check is to follow the Matlab code (pretend you are the computer) and following
(writing out) the loops for the first few terms. You will very quickly see that both
programs as written are correct.
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