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

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11567/997314
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