Instructions to MatLab (2)
MatLab can be used as a calculator and a programming language.
In this section, we demonstrate the uses of MatLab as
a calculator and programming language by an
example of finding the fixed point P=0 of g(x)=x2-e-x+1
by fixed-point iterations.
Use MatLab as a Calculator
MatLab can be used as an expression evaluator. To do this you
simply type a mathematical expression into the command
window. The command window prompt is >>.
To enter an expression, type it after the prompt.
Press the Return key to execute the command.
Editing in command window
- backspacing key -- delete a letter or letters
- left and right arrow keys -- move the cursor
back and forth on the command
line to where a letter needs to be deleted or inserted
- up and down arrow keys -- move up and down on the list of
previous commands to repeat using a command
The fixed-point iteration for this problem is:
xn+1=g(xn)=xn2-e-xn+1.
Start at x0=-1. Compute x1 as follows.
>> x=-1; (";" - not to display the value of x on the window)
>> x=x^2-exp(-x)+1
MatLab responds with
x =
-0.7183
To compute x2, x3, ..., repeat the previous
command by pressing the up arrow key and theReturn key.
Here is what you see after repeating twice.
>> x=x^2-exp(-x)+1
x =
-0.5350
>> x=x^2-exp(-x)+1
x =
-0.4212
Use MatLab as a programming language
To compute x100, we can use for-loop command as
follows.
>> x=-1;
>> for i=1:100, x=x^2-exp(-x)+1, end
The last value of x displayed on the screen is x100.
Use ";" instead of "," after the expression for x if you
do not want to have the list of values for xn listed
on the screen.
If you want to save the sequence {xn} in an array, modified
the previous command as follows.
>> x(1)=-1;
>> for i=1:100, x(i+1)=x(i)^2-exp(-x(i))+1; end
Note that I use ";" after evaluating x(i+1) this time in order not to display
values of x(i+1).
If you want to see x50 and x100, type
>> x(51)
ans =
-0.0382
>> x(101)
ans =
-0.0195
To compute also the error and the relative error En
and Rn, add the formulas after the expression for
xn.
>> P=0;
>> x=-1;
>> for i=1:100,
x=x^2-exp(-x)+1,
E=x-P,
R=E/P,
end
Or
>> P=0;
>> x(1)=-1; E(1)=x(1)-P; R(1)=E(1)/P;
>> for i=1:100,
x(i+1)=x(i)^2-exp(-x(i))+1;
E(i+1)=x(i+1)-P;
R(i+1)=E(i+1)/P;
end
Several commands can be written in one line or multiple lines in
the for-loop. They are executed after the command end.
Save the Text of a MatLab Session
diary file_name causes a copy of all subsequent terminal input
and most of the resulting output to be written on the named
file. diary off suspends it. diary on or diary
file_nameturns it back on.