Solved

# Interpolating a minimum??

Posted on 2006-11-15

Here's a problem I can't quite figure out:

I'm auto-correlating some data with itself to find the periodicity. I slide the data over itself and compute the differencves.

So I end up with an array with values like these:

(0, 423179422, 828300948, 1212609754, 1580431328, 1927976212, 2261045098, 2576547366, 2880291562, 3170884920, 3448407680, 3712453192, 3963129656, 4202858738, 4428796224, 4642141464, 4838897098, 5022294960, 5189647866, 5336120170, 5468966802, 5573601410, 5661172944, 5722015070, 5764204226, 5784805298, 5795386094, 5794255268, 5783184466, 5761355708, 5725745692, 5678340672, 5612707394, 5527855798, 5421991904, 5296806718, 5153282668, 4992479880, 4816736914, 4627262472, 4424397458, 4211164230, 3987799654, 3757131960, 3516443192, 3266828654, 3006790876, 2731835909, 2460333151, 2202466559, 1938545198, 1667642709, 1389832004, 1109712475, 824855728, 588591149, 546361448, 811857393, 1161263940, 1500909693, 1830265354, 2141064765, 2442071178, 2727283919, 3004764138, 3268936897, 3523042222, 3765280899, 3994320860, 4213529495, 4419602464, 4616188975, 4796605032, 4965570485, 5121258994, 5255613245, 5377713032, 5469986089, 5551080124, 5603396265, 5641398544, 5658406913, 5668274054, 5665748491, 19636457355401828, 5047136332677536, 14, 0, 94816986516684800, 2105652297, 60130717272, 94816986516684801, 4785076709733484, 94818019412627324, 9034993454800879124, 4785074604081690, 205958216012529665, 201399947, 47953384, 31244160501548260, 13511005043490927)

In case you're not good at reading number without commans, here's the interesting part:

54: 824,855,728

55: 588,591,149

56: 546,361,448

57: 811,857,393

The values hit a minimum at element 56.

Now that's swell, but if you notice the value at 56 is a heck of a lot closer to #55 than to #57. If we assume a kinda normal and continuous function goes through these points, it sure would be nice to estimate the actual minimum.

I'd like to make an educated guess as to where the actual minimum is, but I can't figure out the math! Dang.

Any formulas appreciated.