Assume we're on a computer using 32-bit floats (or something similar), and I'm converting back and forth between the $n$ coefficients of a polynomial and the corresponding $n$ roots of the polynomial. Doing this conversion will obviously lead to some loss in precision. My question is: will this loss in precision be significant? Or in other words, is converting back and forth between coefficients and roots numerically stable? And does the stability significantly worsen for large $n$?
2026-03-27 16:21:50.1774628510
Is converting between roots and coefficients of a polynomial numerically stable?
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