Page 57 - Numerical Analysis Using MATLAB and Excel

Chapter 2 Root Approximations

% \n prints a blank line before printing x1

fprintf('The next approximation is: %9.6f \n', x1)
fprintf('\n'); % Inserts another blank line
%
fprintf('Rerun the program using this value as your next....
approximation \n');
The following lines show MATLAB’s inquiries and our responses (inputs) for the first two
approximations.

Enter coefficients of P(x) in descending order:
[1 0 −5]
Enter starting value: 2
The next approximation is: 2.250000
Rerun the program using this value as your
next approximation
Enter polynomial coefficients in
descending order: [1 0 −5]
Enter starting value: 2.25
The next approximation is: 2.236111
We observe that this approximation is in close agreement with (2.6).

In Chapter 1 we discussed script files and function files. We recall that a function file is a user−
defined function using MATLAB. We use function files for repetitive tasks. The first line of a
function file must contain the word function followed by the output argument, the equal sign (=),
and the input argument enclosed in parentheses. The function name and file name must be the
same but the file name must have the extension .m. For example, the function file consisting of
the two lines below

function y = myfunction(x)
y=x .^ 3 + cos(3 .* x)
is a function file and must be saved as myfunction.m
We will use the while end loop, whose general form is

while expression
commands ...
end
where the commands ... in the second line are executed as long as all elements in expression of the
first line are true.

We will also be using the following commands:

2−4 Numerical Analysis Using MATLAB® and Excel®, Third Edition
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