Error Bounds for Polynomial Evaluation and Complex Arithmetic
Frank W. J. Olver · IMA Journal of Numerical Analysis · 1986
Explicit and computable strict bounds of a posteriori type are constructed for the evaluation of a polynomial and its derivatives by nested multiplication, using floating-point arithmetic. The polynomial may be real or complex, and may contain errors in its coefficients and argument. Some new error bounds for arithmetic operations with complex numbers are included.