Tikhonov regularization

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I am looking at some C code that adds Tikhonov regularization to a positive definite symmetric matrix.

Like this:

power = (matrix[1][1] + matrix[2][2]);

factor = 0.000136 //Found via trial and error

for(i = 1; i < matrixSize; i++ ) {

matrix[i][i] = matrix[i][i]+( factor * power );

}

I am stuck in understanding what that power means, why have the second and third parts of the diagonal been used? How is this even helping make the numbers more stable?

Thanks for any help.