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.

```

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