dc.contributor.author | Hagele, Klemens | |
dc.date.accessioned | 2008-01-03T13:34:55Z | |
dc.date.available | 2008-01-03T13:34:55Z | |
dc.date.issued | 1999-09-29 | |
dc.identifier.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, pp67 | en |
dc.identifier.other | TCD-CS-1999-47 | |
dc.identifier.uri | http://hdl.handle.net/2262/13021 | |
dc.description.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. | en |
dc.format.extent | 583762 bytes | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en | en |
dc.publisher | Trinity College Dublin, Department of Computer Science | en |
dc.relation.ispartofseries | Computer Science Technical Report | en |
dc.relation.ispartofseries | TCD-CS-1999-47 | en |
dc.relation.haspart | TCD-CS-[no.] | en |
dc.subject | Kronecker?s solution | en |
dc.subject | Newton operator | en |
dc.subject | approximate zero | en |
dc.subject | straight?line programs | en |
dc.subject | height of Diophantine varieties | en |
dc.subject | degree of algebraic varieties | en |
dc.subject | Turing machine complexity | en |
dc.title | Kronecker?s and Newton?s approaches to solving : A first comparison | en |
dc.type | Technical Report | en |
dc.identifier.rssuri | https://www.cs.tcd.ie/publications/tech-reports/reports.99/TCD-CS-1999-47.pdf | |