Numerical Condition of Polynomials in Different Forms

@inproceedings{ZhangNumericalCO,
  title={Numerical Condition of Polynomials in Different Forms},
  author={Hong Zhang}
}
Abstract. The zeros of high-degree polynomials are notoriously sensitive to changes in the coefficients, causing problems for available zero-finding software. In this paper, we study how this sensitivity depends on the polynomial representation. We first extend the algebraic characterization of polynomial pseudozero sets from the power basis to general bases. We show that for a polynomial, the numerical conditions of its values and zeros are closely related and can be visualized simultaneously… CONTINUE READING
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