Is the polynomial so perfidious?

Summary. Wilkinson, in 1], has given a comprehensive account of the numerical difficulties of working with polynomials on a floating point computer. The object of this note is to attempt to rehabilitate the polynomial to a certain extent. In particular it is shown here that polynomial deflation can be performed satisfactorily by a method akin to `backward recursion'. Error analyses and examples are given to illustrate the stability of the process. Received October 4, 1993 / Revised version received July 14, 1993