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An accessible but more advanced discussion of machine arithmetic and roundoff error can be found in Higham Higham (2002).

Interesting and more advanced discussion of the numerical difficulties of finding the roots of polynomials can be found in the article by Wilkinson, “The Perfidious Polynomial” Wilkinson (1984) and in the ripostes from Cohen, “Is the Polynomial so Perfidious?” Cohen (1994) and from Trefethen, “Six myths of polynomial interpolation and quadrature,” (Myth 6) Trefethen (2013).

References
  1. Higham, N. J. (2002). Accuracy and Stability of Numerical Algorithms: Second Edition. SIAM.
  2. Wilkinson, J. H. (1984). The Perfidious Polynomial. In Studies in Mathematics (Vol. 24, pp. 1–28). Mathematical Association of America.
  3. Cohen, A. M. (1994). Is the Polynomial so Perfidious? Numerische Mathematik, 68(2), 225–238. 10.1007/s002110050058
  4. Trefethen, L. N. (2013). Approximation Theory and Approximation Practice. SIAM.
Preface
Stability
Preface
Linear systems of equations