Help in identifying a numerical method

Don11135 · science forum beginner Joined: 24 Mar 2005 Posts: 18

You're right, sum1 = sum2 = 0 to start with. The only thing I left out
is that d_i and d_j are both rounded values:

double d_i = round(x[i] / e) // to nearest integer
double d_j = round(x[j] / e) // to nearest integer

highegg wrote:

highegg · science forum beginner Joined: 11 Feb 2005 Posts: 5

Don wrote:

Don11135 · science forum beginner Joined: 24 Mar 2005 Posts: 18

I was provided with some code for refining the estimate of a initial
value, but I have no clue to what class of numerical method this
belongs. Any suggestions would be greatly appreciated. As you can
tell, I'm not a mathematician, just a programmer trying to understand
some code implementation.

Here's the code:

If I have an array of values, x[] and an initial estimated value e,
which all the values in the x array have a relationship to, then

double sum1, sum2

for(i = 0; i < x.length; i++)
{
double d_i = x[i] / e

for(j = 0; j < x.length; j++)
{
double val = min(i + 1, j + 1) - ((i+1)*(j+1)) / (x.length + 1)

double d_j = x[j] / e

sum1 += val * d_j * x[i]
sum2 += val * d_j * d_i
}
}

// finally the refined value

finalValue = sum1 / sum2

In the first iteration of the j loop, the numerator is increasing by
one (1,2,3,4,5..), in the 2nd iteration, the numerator increases by 2
(2,4,6,8...), in the 3rd iteration, the numerator increases by 3
(3,6,9,12...) and so on. The net result is that val becomes some type
of weighting scheme that is applied to both sum1 and sum2. Eventually,
the final value is calculated by dividing sum1 by sum2.

It appears to me to a way to statistically refine an estimated value.

Thanks in advance,

Don

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