Remember from the theory that if x0 is our guess for the root, our next guess is given by:
tolerance),
or we decide that we have iterated too many times and we aren't going to
find a root (so the number of iterations is larger than
max_count).
Most loops in Java are done with the
Now the details. The three arguments to
The next argument tells how to decide if we should
go through the loop again:
The last argument to
The body of the loop is easy. We calculate our next guess for for
construct:
for ( int count=0;
(Math.abs(f(x)) > tolerance) && ( count < max_count);
count ++) {
x= x - f(x)/fprime(x);
System.out.println("Step: "+count+" x:"+x+" Value:"+f(x));
}
Here is the overview: for takes three arguments - how
to begin, how to end, and what to do in between steps. This is
followed by the ever-present curly braces which contain code that the
Java interpreter executes each time it goes through the loop.
for are separated
by semi-colons. In our case, the first is:
int count=1;
which declares a new integer count and initializes it to 0.
The Java interpreter executes this before the loop is entered.
true for another round and
false to stop looping. Remember our
criteria: either we come close to a root, or we have iterated too many
times. The first criterion can be written:
Math.abs(f(x)) > tolerance
Here we see the absolute value function Math.abs.
The second criterion is:
count < max_count
We need both of these to be true to allow another loop to
occur, so we connect the two boolean statements with the and
operator &&, which returns true only if both
of its arguments are true. So all together, we get:
(Math.abs(f(x)) > tolerance) && (count < max_count);
Notice that the two arguments to && are surrounded by
parenthess. This is a good idea since it makes your code easier
to read, and you don't have to worry about order of operations (which
comes first, > or &&?).
for tells what to do between loops. In
our case, we just need to increment the number of counts:
count ++;
The ++ operator adds one to its argument, so this is the
same as count=count+1;
but is shorter and (when you get used to it) easier to read.
x
according to our formula with:
x= x - f(x)/fprime(x);
We also print out a message for the loop letting the user know what
is going on. The simplest method to print a message is
System.out.println which takes a String as its argument:
System.out.println("Step: "+count+" x:"+x+" Value:"+f(x));
Here we see also a nice way to make Strings using +. For
example, if count is equal to 5, the expression
"Step: "+count; evaluates to "Step: 5". The
line above uses + several times to make the information
message.
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5.7.4 Finishing Up |
David Maxwell,
who is still writing this, would like to
hear your comments and suggestions.