Complete numerical isolation of real zeros in zero-dimensional triangular systems

Authors:
Jin-San Cheng;Xiao-Shan Gao;Chee-Keng Yap
Affiliations:
KLMM, Institute of Systems Science;KLMM, Institute of Systems Science;New York University
Venue:
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Year:
2007

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Abstract

We present a complete numerical algorithm of isolating all the real zeros of a zero-dimensional triangular polynomial system Fn Z[x1…,xn]. Our system Fn is general, with no further assumptions. In particular, our algorithm successfully treat multiple zeros directly in such systems. A key idea is to introduce evaluation bounds and sleeve bounds. We implemented our algorithm and promising experimental results are shown.