Complete numerical isolation of real roots in zero-dimentional triangular systems

• Autores: Jin San Cheng, Xiao-Shan Gao, Chee Keng Yap
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 44, Nº 7, 2009, págs. 768-785
• Idioma: inglés
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• Resumen

  • We present a complete numerical algorithm for isolating all the real zeros of a zero-dimensional triangular polynomial system . Our system Fn is general, with no further assumptions. In particular, our algorithm successfully treats multiple zeros directly in such systems. A key idea is to introduce evaluation bounds and sleeve bounds. We also present a much more efficient algorithm for zero-dimensional triangular systems without multiple roots. We implemented our algorithms, and promising experimental results are shown.