Conditional Structures and Loops - A Concise and Practical Introduction to Programming Algorithms in Java - page 45

Program 2.5 Newton's approximation algorithm
double a = 2.0 , x, xold ;
x=a;
do {
xold = x;
// compute one iteration
x = (xold+a/xold)/2.0;
System . out . println (x) ;
}

while (Math. abs(x − xold) > 1e − 10) ;

1.5
1.4166666666666665
1.4142156862745097
1.4142135623746899
1.4142135623730949

Netwon's method is provably converging very fast under mild assumptions.

2.4.3 Loop statement: for

Often programmers need to repeat a sequence of instructions by changing some
variables by a given increment step. Although this can be done using the former
while / do structures, Java provides a more convenient structure: the for loop.
The generic syntax of a for structure is as follows:

for(initialCondition; booleanPredicate; update)
{
block_instructions;
}

For example, consider computing the cumulative sum S n of the first n integers:

n− 1

i = n ( n

− 1)

S n = .

2

i =0

We have the recurrence equation: S n = n 1+ S n− 1 with S 0 = 0. Therefore to

compute this cumulative sum, we start in reverse from S 0 and get S i by adding
i

−

− 1to S i− 1 for all i ∈{ 1 , ..., n } . Let us use the for structure as follows:

Program 2.6 Cumulative sum

class ForLoop
{ public static void main( String

args [ ] )

int i , n=10;
int cumulLoop=0;
for (i=0;i < n ; i ++) { cumulLoop+=i ; }