Re: tetration and logaritms

Am 10.07.2008 12:57 schrieb Gottfried Helms:

b) Interpolation: in a previous post I discussed a likely
difference of methods, when different interpolation-approaches
depending on the h-parameter are assumed.
You gave a polynomial interpolation approach, which I think is
somehow natural.
But the coefficients at -for instance- x^1 with increasing h
(1,1,1,1,1,...)
can also be interpolated by -for instance- a sine-function of h,
as well as the coefficients at higher powers of x.


My above speculation is useless.

Any interpolation must satisfy its own repeated iteration,
so f°0.5(f°0.5(x)) = f(x) and there is only one unique
solution, at least for powerseries, where f(0) = 0.
This can be seen easily when written out using symbolic
coefficients in the powerseries (there is also an
"uniqueness"-theorem concerning the polynomial inter-
polation)

So this idea does not help to overcome the mentioned
"cross-base-incompatibility"

Sorry - this idea was not well considered

Gottfried
.

Relevant Pages

  • Reconsideration: a false interpolation-paradigm in tetration ?
    ... For the computation of tetration to fractional heightsI employ the diagonalization ... This implements well-known manipulation of the coefficients of formal ... This interpolation follows the common idea of polynomial interpolation resp. ... the series for the logarithm, and see, whether we get the correct series. ...
    (sci.math)
  • Re: Quartic interpolation
    ... You can find a cubic satisfying these conditions. ... is called a "clamped spline". ... "nicest looking" interpolation without unnecessary extremums etc. ... I think that I can find the family of possible coefficients (with one ...
    (sci.math)
  • Re: zero-pad as an interpolation in frequency domain?
    ... equation to show that zero-padding is simply an interpolation in ... interpolation operator. ... you have q additional equidistantly spaced coefficients ... coefficients from your zero-padded spectrum. ...
    (comp.dsp)
  • Re: interpolation accuracy, oversampling and fractional interpolation
    ... interpolation between entries of that table. ... in a practical system with fixed precision ... there is a number of phases beyond which the coefficients won't change ... hypothetical impulse response) that will look more like a windowed sinc ...
    (comp.dsp)
  • Re: tetration and logaritms
    ... first another word on the matrix-method: ... then you have a matrix (of coefficients). ... This is then simply "my" matrix-method..(I collect like powers ... You gave a polynomial interpolation approach, ...
    (sci.math)
Loading