×

Projection of a point onto the intersection of spheres in linear varieties. (English) Zbl 1469.51020

The authors study the general task in the Euclidean \(n\)-space for projection of a point onto the intersection of spheres. They obtain a formula for the distance between a point and the intersection of two spheres in linear varieties. They also derive an explicit formula for the projection of a point onto a sphere, which is the intersection of two spheres in linear varieties.

MSC:

51N20 Euclidean analytic geometry
41A50 Best approximation, Chebyshev systems
41A52 Uniqueness of best approximation
51M05 Euclidean geometries (general) and generalizations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Albert, A. A., Solid Analytic Geometry (1949), McGraw-Hill: McGraw-Hill New York · Zbl 0039.16006
[2] Böttcher, A.; Spitkovsky, I. M., A gentle guide to the basics of two projections theory, Linear Algebra Appl., 432, 6, 1412-1459 (2010) · Zbl 1189.47073
[3] Caseiro, R.; Vicente, M. A. Facas; Vitória, José, Projection method and the distance between two linear varieties, Linear Algebra Appl., 563, 446-460 (2019) · Zbl 1408.51026
[4] Deutsch, F., Best Approximation in Inner Product Spaces (2001), Springer: Springer New York · Zbl 0980.41025
[5] G.-M., F., Cours de Géométrie Élémentaire (1912), J. De Gigord: J. De Gigord Paris · JFM 43.0610.05
[6] Galántai, A., Projectors and Projection Methods (2004), Kluwer Academic Publishers: Kluwer Academic Publishers Boston, MA · Zbl 1055.65043
[7] Glazman, I. M.; Ljubič, Ju. I., Finite-Dimensional Linear Analysis: A Systematic Presentation in Problem Form (2006), Dover Publications: Dover Publications New York · Zbl 1115.46001
[8] Kato, T., Perturbation Theory for Linear Operators (1966), Springer-Verlag: Springer-Verlag Berlin · Zbl 0148.12601
[9] Laurent, P.-J., Approximation et Optimisation (1972), Hermann: Hermann Paris · Zbl 0238.90058
[10] Meyer, C., Matrix Analysis and Applied Linear Algebra (2000), SIAM: SIAM Philadelphia · Zbl 0962.15001
[11] Niewenglowski, B. A., Cours de Géométrie Analytique (1914), Gauthier-Villars et fils: Gauthier-Villars et fils Paris, Deuxième Édition, Tome III · JFM 45.0807.09
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.