Dear all,
Consider this code:
// Define polynomial variable
p = poly(0, 'p', 'roots');
// Define fourth degree polynomial
R = (1 + p)^4;
// Find its roots
z = roots(R)
The result (Scilab 6.0.1) is
z =
-1.0001886
-1. + 0.0001886i
-1. - 0.0001886i
-0.9998114
It should be something closer to
-1.
-1.
-1.
-1.
Using these roots
C = coeff((p-z(1))*(p-z(2))*(p-z(3))*(p-z(4)))
yield seemingly accurate coefficients
C =
1. 4. 6. 4. 1.
but
C - [1 4 6 4 1]
shows the actual error:
ans =
3.775D-15 1.243D-14 1.155D-14 4.441D-15 0.
This is acceptable for the coefficients, but the error in the roots is
too large. Somehow the errors cancel out when assembling back the
polynomial but each individual zero should be closer to the theoretical
value
Is there some way to improve the accuracy?
Regards,
Federico Miyara
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