Kronecker?s and Newton?s approaches to solving : A first comparison
Citation:
Hagele, Klemens. 'Kronecker?s and Newton?s approaches to solving : A first comparison'. - Dublin, Trinity College Dublin, Department of Computer Science, TCD-CS-1999-47, 1999, pp67Download Item:
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Abstract:
In these pages we make a first attempt to compute efficiency of symbolic and numerical analysis procedures
that solve systems of multivariate polynomial equations. In particular, we compare Kronecker?s solution
(from the symbolic approach) with approximate zero theory (introduced by M. Shub & S. Smale as a
foundation of numerical analysis). To this purpose we show upper and lower bounds of the bit length
of approximate zeros. We also introduce efficient procedures that transform local Kronecker?s solution
into approximate zeros and conversely. As an application of our study we exhibit an efficient procedure
to compute splitting fields and Lagrange resolvent of univariate polynomial equations. We remark that
this procedure is obtained by a convenient combination of both approaches (numeric and symbolic) to
multivariate polynomial solving.
Author: Hagele, Klemens
Publisher:
Trinity College Dublin, Department of Computer ScienceType of material:
Technical ReportCollections:
Series/Report no:
Computer Science Technical ReportTCD-CS-1999-47
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