We consider the problem of deciding whether or not a zero locus, X, of multivariate real analytic functions crosses a given r-norm ball in the real n-dimensional affine space. We perform a local study of the problem, and we provide both necessary and sufficient conditions to answer the question. Our conditions derive from the analysis of differential geometric properties of X at the center of the ball. An algorithm to evaluate r-norms distances is proposed.
r-norm bounds and metric properties for zero loci of real analytic functions
Torrente M.;Beltrametti M. C.;
2018-01-01
Abstract
We consider the problem of deciding whether or not a zero locus, X, of multivariate real analytic functions crosses a given r-norm ball in the real n-dimensional affine space. We perform a local study of the problem, and we provide both necessary and sufficient conditions to answer the question. Our conditions derive from the analysis of differential geometric properties of X at the center of the ball. An algorithm to evaluate r-norms distances is proposed.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
CAM-D-17-01746R1.pdf
accesso aperto
Tipologia:
Documento in Post-print
Dimensione
618.22 kB
Formato
Adobe PDF
|
618.22 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
