Program For Bisection Method In Fortran Compilers
Just about every FORTRAN programmer on the planet in those days learned how to do mean and standard deviation for himself, as a homework assignment. Every FORTRAN programmer learned bisection and Newton-Raphson iteration (nowadays called 'Newton's Method') in school. However, you may also use software programs including Fortran, Mathematica. Unfortunately, Windows and Moc OS do not come with a build-in compiler. The C++ sample code for the bisection method is ALG021_bisection.cpp.
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For a person 1.80 m tall in relation to body weight m (in kilograms) Take as an example the calculation of (BMI). The BMI is the body weight in kilograms divided by the square of height in metres. A bathroom scale may have a resolution of one kilogram. We do not know intermediate values – about 79.6 kg or 80.3 kg – but information rounded to the nearest whole number. It is unlikely that when the scale reads 80 kg, someone really weighs exactly 80.0 kg. In normal rounding to the nearest value, the scales showing 80 kg indicates a weight between 79.5 kg and 80.5 kg. The relevant range is that of all real numbers that are greater than or equal to 79.5, while less than or equal to 80.5, or in other words the interval [79.5,80.5].
For a man who weighs 80 kg and is 1.80 m tall, the BMI is about 24.7. With a weight of 79.5 kg and the same height the value is 24.5, while 80.5 kilograms gives almost 24.9. So the actual BMI is in the range [24.5,24.9].
The error in this case does not affect the conclusion (normal weight), but this is not always the position. For example, weight fluctuates in the course of a day so that the BMI can vary between 24 (normal weight) and 25 (overweight). Without detailed analysis it is not possible to always exclude questions as to whether an error ultimately is large enough to have significant influence. Interval arithmetic states the range of possible outcomes explicitly. Simply put, results are no longer stated as numbers, but as intervals that represent imprecise values. The size of the intervals are similar to error bars to a metric in expressing the extent of uncertainty. Simple arithmetic operations, such as basic arithmetic and trigonometric functions, enable the calculation of outer limits of intervals.
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Program bisection implicit none real:: a,b,c,error,f error = 1.0e-06 write( *, *) 'Enter two numbers a and b simultaneously between which the root is to be found ' 10 read( *, *) a,b 15 if (f(a) *f(b).lt. 0) then c =(a +b) / 2.0 else write( *, *) 'Try with another values of a and b ' goto 10 end if if (f(a) *f(c).lt. 0) then b =c else a =c end if if ( abs(b -a).gt. Error) goto 15 write( *, *) 'The root is ',c end program real function f( x) implicit none real::x f = 3 *x + sin(x) - exp(x) end function.