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Interpretable code using Newton-Raphson Method
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I am having troubles with a Java code that must calculate the root square of a given parameter.
However,after some research I found a code that I don't know how was implemented properly.
// read in the command-line argument
double c = Double.parseDouble(args[0]);
double epsilon = 1.0e-15; // relative error tolerance
double t = c; // estimate of the square root of c
// repeatedly apply Newton update step until desired precision is achieved
while (Math.abs(t - c/t) > epsilon *t)
t = (c/t + t) / 2.0;
// print out the estimate of the square root of c
System.out.println(t);
The first thing that I don't understand completely is why they are dividing by two on the 8th line.
t = (c/t + t) / 2.0;
The second thing which I do not understand is the condition from the while loop, to be more precise:
while(Math.abs(t - c/t) > epsilon*t)
Wouldn't be necessary to have only:
while(Math.abs(t - c/t) > epsilon)
java newtons-method
asked Mar 27 at 16:42
Tr909Tr909
91 bronze badge
add a comment |
I am having troubles with a Java code that must calculate the root square of a given parameter.
However,after some research I found a code that I don't know how was implemented properly.
// read in the command-line argument
double c = Double.parseDouble(args[0]);
double epsilon = 1.0e-15; // relative error tolerance
double t = c; // estimate of the square root of c
// repeatedly apply Newton update step until desired precision is achieved
while (Math.abs(t - c/t) > epsilon *t)
t = (c/t + t) / 2.0;
// print out the estimate of the square root of c
System.out.println(t);
The first thing that I don't understand completely is why they are dividing by two on the 8th line.
t = (c/t + t) / 2.0;
The second thing which I do not understand is the condition from the while loop, to be more precise:
while(Math.abs(t - c/t) > epsilon*t)
Wouldn't be necessary to have only:
while(Math.abs(t - c/t) > epsilon)
java newtons-method
asked Mar 27 at 16:42
Tr909Tr909
91 bronze badge
Where did you get thatepsilon*tfrom? What does this document/article wrote about this expression and why the factor*tis used?
– Progman
Mar 27 at 18:58
add a comment |
I am having troubles with a Java code that must calculate the root square of a given parameter.
However,after some research I found a code that I don't know how was implemented properly.
// read in the command-line argument
double c = Double.parseDouble(args[0]);
double epsilon = 1.0e-15; // relative error tolerance
double t = c; // estimate of the square root of c
// repeatedly apply Newton update step until desired precision is achieved
while (Math.abs(t - c/t) > epsilon *t)
t = (c/t + t) / 2.0;
// print out the estimate of the square root of c
System.out.println(t);
The first thing that I don't understand completely is why they are dividing by two on the 8th line.
t = (c/t + t) / 2.0;
The second thing which I do not understand is the condition from the while loop, to be more precise:
while(Math.abs(t - c/t) > epsilon*t)
Wouldn't be necessary to have only:
while(Math.abs(t - c/t) > epsilon)
java newtons-method
asked Mar 27 at 16:42
Tr909Tr909
91 bronze badge
I am having troubles with a Java code that must calculate the root square of a given parameter.
However,after some research I found a code that I don't know how was implemented properly.
// read in the command-line argument
double c = Double.parseDouble(args[0]);
double epsilon = 1.0e-15; // relative error tolerance
double t = c; // estimate of the square root of c
// repeatedly apply Newton update step until desired precision is achieved
while (Math.abs(t - c/t) > epsilon *t)
t = (c/t + t) / 2.0;
// print out the estimate of the square root of c
System.out.println(t);
The first thing that I don't understand completely is why they are dividing by two on the 8th line.
t = (c/t + t) / 2.0;
The second thing which I do not understand is the condition from the while loop, to be more precise:
while(Math.abs(t - c/t) > epsilon*t)
Wouldn't be necessary to have only:
while(Math.abs(t - c/t) > epsilon)
java newtons-method
java newtons-method
asked Mar 27 at 16:42
Tr909Tr909
91 bronze badge
asked Mar 27 at 16:42
Tr909Tr909
91 bronze badge
asked Mar 27 at 16:42
Tr909Tr909
91 bronze badge
asked Mar 27 at 16:42
Tr909Tr909
91 bronze badge
asked Mar 27 at 16:42
Tr909Tr909
91 bronze badge
91 bronze badge
Where did you get thatepsilon*tfrom? What does this document/article wrote about this expression and why the factor*tis used?
– Progman
Mar 27 at 18:58
add a comment |
Where did you get thatepsilon*tfrom? What does this document/article wrote about this expression and why the factor*tis used?
– Progman
Mar 27 at 18:58
Where did you get that
epsilon*t from? What does this document/article wrote about this expression and why the factor *t is used?– Progman
Mar 27 at 18:58
Where did you get that
epsilon*t from? What does this document/article wrote about this expression and why the factor *t is used?– Progman
Mar 27 at 18:58
add a comment |
1 Answer
1
active
oldest
votes
t = (c/t + t) / 2.0;
This is used to calculate the average/mean of the two values c/t and t. The value is stored in the variable t for the next loop iteration. Use a System.out.println() call inside the while loop to check the values of t and c/t before this line and the values after this line.
answered Mar 27 at 18:57
ProgmanProgman
7,2573 gold badges21 silver badges37 bronze badges
add a comment |
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1 Answer
1
active
oldest
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oldest
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active
oldest
votes
t = (c/t + t) / 2.0;
This is used to calculate the average/mean of the two values c/t and t. The value is stored in the variable t for the next loop iteration. Use a System.out.println() call inside the while loop to check the values of t and c/t before this line and the values after this line.
answered Mar 27 at 18:57
ProgmanProgman
7,2573 gold badges21 silver badges37 bronze badges
add a comment |
t = (c/t + t) / 2.0;
This is used to calculate the average/mean of the two values c/t and t. The value is stored in the variable t for the next loop iteration. Use a System.out.println() call inside the while loop to check the values of t and c/t before this line and the values after this line.
answered Mar 27 at 18:57
ProgmanProgman
7,2573 gold badges21 silver badges37 bronze badges
add a comment |
t = (c/t + t) / 2.0;
This is used to calculate the average/mean of the two values c/t and t. The value is stored in the variable t for the next loop iteration. Use a System.out.println() call inside the while loop to check the values of t and c/t before this line and the values after this line.
answered Mar 27 at 18:57
ProgmanProgman
7,2573 gold badges21 silver badges37 bronze badges
t = (c/t + t) / 2.0;
This is used to calculate the average/mean of the two values c/t and t. The value is stored in the variable t for the next loop iteration. Use a System.out.println() call inside the while loop to check the values of t and c/t before this line and the values after this line.
answered Mar 27 at 18:57
ProgmanProgman
7,2573 gold badges21 silver badges37 bronze badges
answered Mar 27 at 18:57
ProgmanProgman
7,2573 gold badges21 silver badges37 bronze badges
answered Mar 27 at 18:57
ProgmanProgman
7,2573 gold badges21 silver badges37 bronze badges
answered Mar 27 at 18:57
ProgmanProgman
7,2573 gold badges21 silver badges37 bronze badges
7,2573 gold badges21 silver badges37 bronze badges
add a comment |
add a comment |
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Where did you get that
epsilon*tfrom? What does this document/article wrote about this expression and why the factor*tis used?– Progman
Mar 27 at 18:58