The circular complex centered form

The centered form for real interval functions was first defined by R. E. Moore in his bookInterval Analysis [6]. Based on numerical experiments he conjectured that the centered form converges quadratically on the width of the range interval. The conjecture was first proved by Hansen [4] and later in a more general form by Miller [5]. In this paper a centered form is developed for circular complex interval polynomials (see [3]). This form is shown to always be an improvement on the power sum evaluation in contrast to the real case. The quadratic convergence of this form on the radius of the circular complex range interval is proved and some numerical examples are presented.