Tighter Bounds of Errors of Numerical Roots
Sasaki, Tateaki
Japan J. Indust. Appl. Math., Tome 24 (2007) no. 1, p. 219-226 / Harvested from Project Euclid
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Let $P(z)$ be a monic univariate polynomial over $\mathbf{C}$, of degree $n$ and having roots $\zeta_1,\ldots,\zeta_n$. Given approximate roots $z_1,\ldots,z_n$, with $\zeta_i \simeq z_i$ ($i=1,\ldots,n$), we derive a very tight upper bound of $|\zeta_i - z_i|$, by assuming that $\zeta_i$ has no close root. The bound formula has a similarity with Smale's and Smith's formulas. We also derive a lower bound of $|\zeta_i - z_i|$ and a lower bound of $\min\{|\zeta_j - z_i|\mid j \neq i\}$.
Publié le : 2007-06-14
Classification:  
@article{1197908782,
     author = {Sasaki, Tateaki},
     title = {Tighter Bounds of Errors of Numerical Roots},
     journal = {Japan J. Indust. Appl. Math.},
     volume = {24},
     number = {1},
     year = {2007},
     pages = { 219-226},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1197908782}
}

Sasaki, Tateaki. Tighter Bounds of Errors of Numerical Roots. Japan J. Indust. Appl. Math., Tome 24 (2007) no. 1, pp.  219-226. http://gdmltest.u-ga.fr/item/1197908782/