Re: restricting interpolating functions to be positive

*To*: mathgroup at smc.vnet.net*Subject*: [mg106587] Re: restricting interpolating functions to be positive*From*: Ray Koopman <koopman at sfu.ca>*Date*: Sun, 17 Jan 2010 07:12:03 -0500 (EST)*References*: <higdjs$kfi$1@smc.vnet.net> <201001131058.FAA06854@smc.vnet.net>

On Jan 15, 12:18 am, schochet123 <schochet... at gmail.com> wrote: > On Jan 14, 12:46 pm, DrMajorBob <btre... at austin.rr.com> wrote: > >> For some data, that works pretty well; for other samples >> it has HUGE peaks, reaching far above any of the data: > > This problem can be avoided by using a transformation that > is close to the identity for positive values: > > trans[x_] = (Sqrt[1 + x^2] + x)/2 > > inv[y_] = (4 y^2 - 1)/(4 y) There's a whole family of transformations here: trans[c_,x_] = (Sqrt[4c + x^2) + x)/2 inv[c_,y_] = y - c/y Extremely small values of c give results that approach those obtained by chopping the interpolation at 0.

**References**:**Re: restricting interpolating functions to be positive***From:*Noqsi <jpd@noqsi.com>