Pré-prints de 2003
2003.01 - A pirâmide de Pascal (
Luzitelma Maria Barbosa de Castro e
Praciano-Pereira, Tarcisio )
Mostramos uma generalização do Triângulo de Pascal em que pisos
de uma pirâmide governam a distribuição das potências
de um trinômio.
2003.02 - A new projector (Medeiros, J.C.O., Rodrigues dos Santos, S.,
In this paper we present a new projector by modifying
a previous construction of an interpolation projector of ours.
This new projector produces quasi-convolution splines tangent to the target function.
2003.03 - Existence of compact support splines (Medeiros, J.C.O.,
Rodrigues dos Santos, S., Praciano-Pereira, T.)
We shall develop here the construction of a compact support convolution
spline kernel, that is, a kernel, a function whose integral is one,
with compact support that is a spline. These objects are the nth-power
by convolution of characteristic functions of intervals.
Convolution spline kernels are not really new, they appeared
in a paper of one of the authors of this paper, in 1994,
and at the same time in papers of others authors, the main reason for
this paper lies in the construction itself, a very simple one we found
using distribution derivatives which we believe will open the way for
a simple algorithm to implement these splines in a computer program.
2003.04 - Precision results regarding an interpolation projector
(Medeiros, J.C.O., Rodrigues dos Santos, S., Praciano-Pereira, T.)
In this paper we present a modified version of convolution spline basis,
but now these convolution splines are tangent to the target
function f at the precision points. This has been done by constructing
a spline approximation of f' and obtaining f by integration.
The algorithm is more effective but has to be improved yet.
In the previous process the spline function passed by
the precision points with zero derivative, with good precision
regarding the energy, but bad visual performance. Graphs are
supplied to make the comparison clear.