Re: Are there multiple roots?

In article <1156650930.680308.267980@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
carlos@xxxxxxxxxxxx writes:
Have you every thought about doing your root searching
via the Winding Number theorem and simply Cauchy integrals?
For Zeke polynomial, f(z) = (z-1)...(z-20). I compute in
double precision a winding number for an appropriately chosen
circular contour as (19.9999999999999, 1.424416140594076E-015).
Since we have a polynomial, the real part tells that we have
at most 20 roots.

By suitably deformation and translation of the contour, you can
find the roots. For z=1, I find



val = ( 1.00000000000000 , 3.174127627403323E-015)
z = ( 1.00000000000000 , 2.663980147588063E-015)


(snip)

and all coefficients can be fairly well represented as
double floats. By contrast, the mantissas of many of
coefficients of P60 suffer significant truncation when
chopped off to 16 places.

Well, of course! If you expand the polynomial such that the
coefficients can't be accurately represented in the precision
of the computation, then you're going to get the wrong answer.
Geez, this isn't rocket science.

--
Steve
http://troutmask.apl.washington.edu/~kargl/
.

Relevant Pages

  • Re: Are there multiple roots?
    ... via the Winding Number theorem and simply Cauchy integrals? ... at most 20 roots. ... Mathematica in standard FP precision ... and all coefficients can be fairly well represented as ...
    (sci.math.num-analysis)
  • 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: Transformer coupling coefficients
    ... cores, ... (e.g. parallel windings above and below another winding) ... I often see the leakage inductance of a ferrite quoted as being equal to ... can back out from leakage inductance to coupling coefficients. ...
    (sci.electronics.design)
  • Re: Maxima - precision
    ... You are computing the roots of a polynomial in machine precision. ... But maybe your polynomials are not nasty. ...
    (sci.math.symbolic)
  • Re: Transformer coupling coefficients
    ... cores, ... (e.g. parallel windings above and below another winding) ... I often see the leakage inductance of a ferrite quoted as being equal to ... can back out from leakage inductance to coupling coefficients. ...
    (sci.electronics.design)
Loading