I am not so familiar with 'interpolation' math, albeit I grasp the underlying logic. I was wondering if there is a rule of thumb in the choice of the number of neighbor points to use in IDW interpolation method. This site (http://www.quantdec.com/SYSEN597/GTKAV/section9/chapter_29b.htm) provides a good description of the method, and of the difference between a fixed search radius or a variable one (the latter depending on the specified number of neighbors). But I am still wondering on what basis the number of neighbors has to be chosen. Does it somehow depend on the number of original data points? By the way, I use arcGIS 10.1. w/ advanced license.
You should read help for the function in ArcGIS here. However, you could define number of neighbor points (cells) and the function will take the exact number of nearest points. Or you could define search radius in i. e. meters and all the points (cells) that fit into this radius will be taken into the interpolation.
To choose the amount of neighbours, it depends of type of input data. If you choose many neighbours i.e. for interpolating DEM, the result will be more smooth than if you choose less. Otherway, if you will choose many neighbours, the result will have bigger deviation compare to interpolation with less neighbours. Other example, if you have some meteostations as a points and there is one that doesn'n have data and you want to interpolate it using IDW, imagine the influence of input neighbours. This IDW method strongly depends on spatial resolution of data. What kind of data do you have?