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# Balík: liblip2 (2.0.0-1.1)

## 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.

## Ostatné balíky súvisiace s balíkom liblip2

 závisí odporúča navrhuje enhances
• dep: libc0.1 (>= 2.3) [kfreebsd-amd64, kfreebsd-i386]
knižnica Embedded GNU C - zdieľané knižnice
tiež virtuálny balík poskytovaný balíkom libc0.1-udeb
• dep: libc6 (>= 2.13) [s390x]
knižnica Embedded GNU C - zdieľané knižnice
tiež virtuálny balík poskytovaný balíkom libc6-udeb
dep: libc6 (>= 2.4) [armhf]
dep: libc6 (>= 2.7-1) [nie armhf, ia64, kfreebsd-amd64, kfreebsd-i386, s390x]
• dep: libc6.1 (>= 2.7-1) [ia64]
knižnica Embedded GNU C - zdieľané knižnice
tiež virtuálny balík poskytovaný balíkom libc6.1-udeb
• dep: libgcc1 (>= 1:4.1.1) [s390x]
podporná knižnica GCC
dep: libgcc1 (>= 1:4.1.1-21) [nie armel, armhf, kfreebsd-amd64, kfreebsd-i386, s390x]
dep: libgcc1 (>= 1:4.3) [armel]
dep: libgcc1 (>= 1:4.4) [kfreebsd-amd64, kfreebsd-i386]
dep: libgcc1 (>= 1:4.4.0) [armhf]
• dep: libstdc++6 (>= 4.1.1) [s390x]
štandardná knižnica C++ GNU v3
dep: libstdc++6 (>= 4.1.1-21) [nie armel, armhf, kfreebsd-amd64, kfreebsd-i386, s390x]
dep: libstdc++6 (>= 4.3) [armel]
dep: libstdc++6 (>= 4.4) [kfreebsd-amd64, kfreebsd-i386]
dep: libstdc++6 (>= 4.4.0) [armhf]
• dep: libunwind7 (>= 0.98.5-6) [ia64]
knižnica na určenie postupnosti volania programu - dynamická verzia

## Stiahnuť liblip2

Stiahnuť pre všetky dostupné architektúry
Architektúra Veľkosť balíka Nainštalovaná veľkosť Súbory
amd64 295.1 kB488.0 kB [zoznam súborov]
armel 292.7 kB476.0 kB [zoznam súborov]
armhf 284.7 kB400.0 kB [zoznam súborov]
i386 292.6 kB476.0 kB [zoznam súborov]
ia64 325.3 kB616.0 kB [zoznam súborov]
kfreebsd-amd64 296.1 kB478.0 kB [zoznam súborov]
kfreebsd-i386 294.0 kB464.0 kB [zoznam súborov]
mips 297.2 kB516.0 kB [zoznam súborov]
mipsel 297.5 kB516.0 kB [zoznam súborov]
powerpc 303.4 kB508.0 kB [zoznam súborov]
s390 295.8 kB484.0 kB [zoznam súborov]
s390x 300.1 kB486.0 kB [zoznam súborov]
sparc 292.4 kB480.0 kB [zoznam súborov]