Re: Osculating/Hermite Interpolation on sampled data
in article GpCdnbQrNNy_OqbeRVn-hw@xxxxxxxxxxxx, snappy at glad@xxxxxx wrote
on 09/29/2005 04:34:
> Speaking about continuity when using interpolating polynomials make sense
> since we can set up equations of constraints for this when constructing
> the polynomials (such as for splines).
you might refer to Olli Niemitalo's paper on polynomial interpolation at
http://www.biochem.oulu.fi/~oniemita/dsp/deip.pdf
it is a definite improvement on an earlier paper on the same topic that
Duane Wise and i did sometime in the 90s. ours doesn't live on the web, but
i can send you a copy if you want.
> When using windowed sinc interpolation, does it make sense to talk about
> interpolation continuity?
sure.
> If so, how is this measured?
you mean how is this determined? the sinc() function is fully continuous
(the 0/0 singularity is a "removable" singularity) in all of its
derivatives. if the window is continuous (at least to the point where it
ends), then the windowed sinc() is continuous (at least to the point where
it ends).
--
r b-j rbj@xxxxxxxxxxxxxxxxxxxx
"Imagination is more important than knowledge."
.
Relevant Pages
- Re: Osculating/Hermite Interpolation on sampled data
... Speaking about continuity when using interpolating polynomials make sense ... since we can set up equations of constraints for this when constructing ... When using windowed sinc interpolation, does it make sense to talk about ...
(comp.dsp) - Re: Osculating/Hermite Interpolation on sampled data
... > Speaking about continuity when using interpolating polynomials make sense ... > since we can set up equations of constraints for this when constructing ... > When using windowed sinc interpolation, does it make sense to talk about ...
(comp.dsp) - Re: Secant method vs Newtons method
... It is found that the Secant Method is obtained using zero order NIH and higher order methods with increasingly higher order error terms are obtained by using First or Second Order NIH. ... The simple innovation which I am using in NIH, and which is indicated by the word Normalized, is that I am using for interpolation the two point Hermite Interpolating Polynomial interpolating the function and some of its derivatives on a normalized interval by simply mapping the bracketing interval to the normalized interval each iteration. ... This allows use of the same interpolation formula every step of the iterative search for the root by evaluating the root of the Hermite polynomial interpolating the inverse function and its first or even second derivatives on two points within the normalized interval. ... I have described this on my website www.numerical-algorithms.com under the section "Root Finding Using Inverse Normalized Hermite Interpolation" and present an example where I compute the roots of the Legendre polynomials. ...
(sci.math.num-analysis) - Re: Integer-Valued Polynomials
... variables and for general fields? ... has little to do with the question of interpolation. ... Interpolating polynomials in many variables, ... A tensor product of nonsingular ...
(sci.math) - Re: Secant method vs Newtons method
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