# liblip 2.0.0-1.1ubuntu1 source package in Ubuntu

## Changelog

```liblip (2.0.0-1.1ubuntu1) trusty; urgency=low

* Use debhelper and its autoreconf helper to correctly build shared
libraries on newer arches, resolving FTBFS.
-- Daniel T Chen <email address hidden>   Mon, 24 Mar 2014 16:12:32 -0400```

Daniel T Chen
Trusty
Original maintainer:
Ubuntu Developers
Architectures:
any
Section:
math
Urgency:
Low Urgency

## See full publishing history Publishing

Series Pocket Published Component Section
Trusty release universe math

## Builds

File Size SHA-256 Checksum
liblip_2.0.0-1.1ubuntu1.diff.gz 4.8 KiB 106cbd0e4d3ef624f789bdb50194b1db96cbe3cb46bb67eb39bce21df685e653

## Binary packages built by this source

liblip-dev: reliable interpolation of multivariate scattered data

Lip interpolates scattered multivariate data with a Lipschitz function.
.
Methods of interpolation of multivariate scattered data are scarce.
The programming library Lip implements a
new method by G. Beliakov, which relies on building reliable lower and
upper approximations of Lipschitz functions. If we assume that the
function that we want to interpolate is Lipschitz-continuous, we can
provide tight bounds on its values at any point, in the worse case
scenario. Thus we obtain the interpolant, which approximates the unknown
Lipschitz function f best in the worst case scenario. This translates
into reliable learning of f, something that other methods cannot do (the
error of approximation of most other methods can be infinitely large,
depending on what f generated the data).
.
Lipschitz condition implies that the rate of change of the function is
bounded:
.
|f(x)-f(y)|<M||x-y||.
.
It is easily interpreted as the largest slope of the function f. f needs
not be differentiable.
.
The interpolant based on the Lipschitz properties of the function is
piecewise linear, it possesses many useful properties, and it is shown
that it is the best possible approximation to f in the worst case
scenario. The value of the interpolant depends on the data points in the
immediate neigbourhood of the point in question, and in this sense, the
method is similar to the natural neighbour interpolation.
.
There are two methods of construction and evaluation of the interpolant.
The explicit method processes all data points to find the neighbours of
the point in question. It does not require any preprocessing, but the
evaluation of the interpolant has linear complexity O(K) in terms of the
number of data.
.
"Fast" method requires substantial preprocessing in the case of more
than 3-4 variables, but then it provides O(log K) evaluation time, and
thus is suitable for very large data sets (K of order of 500000) and
modest dimension (n=1-4). For larger dimension, explicit method becomes
practically more efficient. The class library Lip implements both fast
and explicit methods.

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