0
$\begingroup$

Suppose we have given constants $A_i, x_i (i=1..N)$

Is it possible to approximately calculate the sum of N gaussians in less than N iterations for any x? (may be with some preprocessing)

$$\sum_{i=1}^{N}A_i e^{-(x-x_i)^2}$$

The same question for 2D case $$\sum_{i=1}^{N}A_i e^{-(x-x_i)^2-(y-y_i)^2}$$

$\endgroup$
  • $\begingroup$ Google (scholar) for "fast gaussian summation" or "fast gauss transform". $\endgroup$ – Hans Engler Dec 6 '15 at 15:21
0
$\begingroup$

If the $A_i$, $x_i$ and $y_i$ can take arbitrary values then it is hopeless because you even need $N$ iterations merely to read the input.

If (some of) the Gaussians have the same distribution then their sum can be expressed as a single Gaussian.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.