r-norm bounds and metric properties for zero loci of real analytic functions
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/49655DOI: 10.1016/j.cam.2018.01.001
ISSN: 0377-0427
Publisher
Elsevier
Date
2018-07Funders
Ministerio de Economía y Competitividad
Bibliographic citation
Torrente, M., Beltrametti, M.C. & Sendra, J.R. 2018, “r-norm bounds and metric properties for zero loci of real analytic functions”, Journal of Computational and Applied Mathematics, vol. 336, pp. 375-393.
Keywords
Matrix norms equivalence
Zero locus of real analytic functions
Crossing area conditions
r-norm distance
Description / Notes
A major part of this work was developed while J.R. Sendra was visiting, in the frame of GNSAGA—Istituto Nazionale di Alta Matematica, the University of Genova, and while M.C. Beltrametti and M. Torrente were visiting the University
of Alcalá, in the frame of the project Giner de los Rios and of GNSAGA—Istituto Nazionale di Alta Matematica.
Project
info:eu-repo/grantAgreement/MINECO//MTM2014-54141-P/ES/CONSTRUCCIONES ALGEBRO-GEOMETRICAS: FUNDAMENTOS, ALGORITMOS Y APLICACIONES/
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/acceptedVersion
Publisher's version
https://doi.org/10.1016/j.cam.2018.01.001Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2018 Elsevier
Access rights
info:eu-repo/semantics/openAccess
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.
Files in this item
Files | Size | Format |
|
---|---|---|---|
r_norm_Torrente_J_Comput_Appl_ ... | 921.7Kb |
|
Files | Size | Format |
|
---|---|---|---|
r_norm_Torrente_J_Comput_Appl_ ... | 921.7Kb |
|
Collections
- MATEMATIC - Artículos [172]