×

The Newton’s method interval single-step procedure for bounding polynomial zeros simultaneously. (English) Zbl 1334.65080

Summary: The existing interval symmetric single-step procedure IMW established [M. Monsi and M. A. Wolfe, Appl. Math. Comput. 25, No. 4, 333–346 (1988; Zbl 0637.65040)] has a rate of convergence at least three. In this paper, the rate of convergence of this procedure is increased by introducing a Newton’s method (NM) at the beginning of the procedure. It is used only once in the first iteration. The rate of convergence of NM is two. Based on the numerical results, this new procedure called INMW performed better than does IMW, with the rate of convergence possibly higher than three.

MSC:

65H04 Numerical computation of roots of polynomial equations
65G30 Interval and finite arithmetic

Citations:

Zbl 0637.65040

Software:

IZSS1; INTLAB
PDFBibTeX XMLCite
Full Text: DOI Link