Lagrange multipliers and other higher-order interpolation methods

I am wondering if there are any applications for higher-order Lagrange 
approximating polynomials in digital signal processing or image 
re-sampling.  I know that Lagrange multipliers are used to some extent 
in the construction of FIR filters, and are also used in bicubic 
interpolation.  However, is there an application involving higher order 
Lagrange polynomials?

Does anyone know of a good reference book dealing with bicubic and/or 
higher order Lagrange?  Does using higher order improve the accuracy 
with 2D, or do I still have to deal with the Runge phenomenon?

Nicholas

On Oct 27, 3:27&#4294967295;am, Nicholas Kinar <n.ki...@usask.ca> wrote:
> I am wondering if there are any applications for higher-order Lagrange
> approximating polynomials in digital signal processing or image
> re-sampling. &#4294967295;I know that Lagrange multipliers are used to some extent
> in the construction of FIR filters, and are also used in bicubic
> interpolation. &#4294967295;However, is there an application involving higher order
> Lagrange polynomials?
>
> Does anyone know of a good reference book dealing with bicubic and/or
> higher order Lagrange? &#4294967295;Does using higher order improve the accuracy
> with 2D, or do I still have to deal with the Runge phenomenon?
>
> Nicholas

hi nicholas,
                   in two dimensional channel estimation
methods..higher order interpolation techniques are used.please look
out for them. Long back i saw one pdf of some company on
internet..about 2d channel estimation.

thanks
particlereddy

Thanks, particlereddy!  I'll do a search for these techniques on Google. 
  This sounds very interesting.  Thank you for drawing my attention to this!

Nicholas


>> Nicholas
> 
> hi nicholas,
>                    in two dimensional channel estimation
> methods..higher order interpolation techniques are used.please look
> out for them. Long back i saw one pdf of some company on
> internet..about 2d channel estimation.
> 
> thanks
> particlereddy

Nicholas, note that "Lagrange multiplier" is a term from numerical 
optimization with a meaning totally unrelated to Lagrange 
polynomials.


Martin

-- 
Quidquid latine scriptum est, altum videtur.

Of course, there are different meanings ascribed to a series of methods 
which are all named "Lagrange."  The name is ubiquitous in science and 
engineering.

Your comment is most appropriate for this discussion thread on comp.dsp. 
  Thanks Martin!

Nicholas


Martin Eisenberg wrote:
> Nicholas, note that "Lagrange multiplier" is a term from numerical 
> optimization with a meaning totally unrelated to Lagrange 
> polynomials.
> 
> 
> Martin
>