Natural Science Forum / Physics / Acoustics / March 2006

i am doing some research on acoustics and particularly the nature of
room reverberation. this led me to some harsh number crunching using
matlab.
i am working with polynomials having hundreds of terms and very high
powers in the range of 800 to 2000.
i am particularly interested in the position of the roots relative to
the unit circle. Thus i am using roots() a matlab funtion to compute
the roots of the polynomial. This seems to be working fine (altough i
presume i have rounding errors).
Now my intention is to position all roots inside the unti circle by
computing the reciprocal of the roots outside and then recompute the
coefficients of the new polynomial using the poly() function
This however is leading to a false result. The functions roots() and
poly(), seem to work well when i tested them with small polynomials as
shown below:

polycoeff =

   1.0000    0.6000    0.4000    0.2000    0.1000

polyroots =

  0.1340 + 0.5544i
  0.1340 - 0.5544i
 -0.4340 + 0.3450i
 -0.4340 - 0.3450i

originalpoly =

   1.0000    0.6000    0.4000    0.2000    0.1000

Is this a problem of rounding? I even tried using some other code i
found on matlab's file exchange poly1() and roots1() but still same
false result occur. The coefficients of the resulting polynomial range
from very small 10^-40 to 10^128 which is not the case with my
polynomials which have the largest coeff at 1. Any help greatly
appreciated.

jeremy