## Version 1.1.0

• Single
• Double

### PA16 Complex coeﬃcients: all roots by the method of Madsen and Reid

To ﬁnd all the real and complex roots of a polynomial with complex coeﬃcients, i.e. calculate the zeros of

${a}_{0}+{a}_{1}x+{a}_{2}{x}^{2}+...+{a}_{n}{x}^{n}=0$

The user can supply error bounds on the coeﬃcients of the polynomial and the routine returns bounds on the moduli of the errors in the roots. The roots are found by the method of Madsen and error bounds by the application of Rouche’s theorem.

Precision: At least 8-byte arithmetic is recommended.