English   español  
Por favor, use este identificador para citar o enlazar a este item: http://hdl.handle.net/10261/170597
COMPARTIR / IMPACTO:
Estadísticas
logo share SHARE logo core CORE   Add this article to your Mendeley library MendeleyBASE

Visualizar otros formatos: MARC | Dublin Core | RDF | ORE | MODS | METS | DIDL
Exportar a otros formatos:
Título

On the regularity of the covariance matrix of a discretized scalar field on the sphere

AutorBilbao Ahedo, Juan Daniel; Barreiro, R. Belén ; Herranz, D. ; Vielva, P. ; Martínez-González, Enrique
Fecha de publicación2017
EditorInstitute of Physics Publishing
CitaciónJournal of Cosmology and Astroparticle Physics 2017: 022 (2017)
ResumenWe present a comprehensive study of the regularity of the covariance matrix of a discretized field on the sphere. In a particular situation, the rank of the matrix depends on the number of pixels, the number of spherical harmonics, the symmetries of the pixelization scheme and the presence of a mask. Taking into account the above mentioned components, we provide analytical expressions that constrain the rank of the matrix. They are obtained by expanding the determinant of the covariance matrix as a sum of determinants of matrices made up of spherical harmonics. We investigate these constraints for five different pixelizations that have been used in the context of Cosmic Microwave Background (CMB) data analysis: Cube, Icosahedron, Igloo, GLESP and HEALPix, finding that, at least in the considered cases, the HEALPix pixelization tends to provide a covariance matrix with a rank closer to the maximum expected theoretical value than the other pixelizations. The effect of the propagation of numerical errors in the regularity of the covariance matrix is also studied for different computational precisions, as well as the effect of adding a certain level of noise in order to regularize the matrix. In addition, we investigate the application of the previous results to a particular example that requires the inversion of the covariance matrix: the estimation of the CMB temperature power spectrum through the Quadratic Maximum Likelihood algorithm. Finally, some general considerations in order to achieve a regular covariance matrix are also presented.
DescripciónarXiv:1701.06617v2
Versión del editorhttps://doi.org/10.1088/1475-7516/2017/02/022
URIhttp://hdl.handle.net/10261/170597
Identificadoresdoi: 10.1088/1475-7516/2017/02/022
e-issn: 1475-7516
Aparece en las colecciones: (IFCA) Artículos
Ficheros en este ítem:
Fichero Descripción Tamaño Formato  
regulspher.pdf932,23 kBAdobe PDFVista previa
Visualizar/Abrir
Mostrar el registro completo
 


NOTA: Los ítems de Digital.CSIC están protegidos por copyright, con todos los derechos reservados, a menos que se indique lo contrario.