- -

Strategies for spectrum slicing based on restarted Lanczos methods

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

Strategies for spectrum slicing based on restarted Lanczos methods

Mostrar el registro sencillo del ítem

Ficheros en el ítem

Thumbnail
Nombre: slice_tr.pdf
Tamaño: 340.5Kb
Formato: PDF
Descripción: Versión del Autor.
Abrir
[Cerrado]
Nombre: Campos;Román - ...
Tamaño: 341.4Kb
Formato: PDF
Descripción: Versión editorial
Solicitar una copia al autor
dc.contributor.author Campos González, Maria Camen es_ES
dc.contributor.author Román Moltó, José Enrique es_ES
dc.date.accessioned 2014-05-08T12:28:31Z
dc.date.issued 2012-06
dc.identifier.issn 1017-1398
dc.identifier.uri http://hdl.handle.net/10251/37323
dc.description.abstract In the context of symmetric-definite generalized eigenvalue problems, it is often required to compute all eigenvalues contained in a prescribed interval. For large-scale problems, the method of choice is the so-called spectrum slicing technique: a shift-and-invert Lanczos method combined with a dynamic shift selection that sweeps the interval in a smart way. This kind of strategies were proposed initially in the context of unrestarted Lanczos methods, back in the 1990's. We propose variations that try to incorporate recent developments in the field of Krylov methods, including thick restarting in the Lanczos solver and a rational Krylov update when moving from one shift to the next. We discuss a parallel implementation in the SLEPc library and provide performance results. © 2012 Springer Science+Business Media, LLC. es_ES
dc.description.sponsorship This work was supported by the Spanish Ministerio de Ciencia e Innovacion under grant TIN2009-07519. en_EN
dc.format.extent 17 es_ES
dc.language Inglés es_ES
dc.publisher Springer Verlag (Germany) es_ES
dc.relation.ispartof Numerical Algorithms es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Large-scale eigenvalue computations es_ES
dc.subject Parallel numerical libraries es_ES
dc.subject Spectrum slicing es_ES
dc.subject.classification CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL es_ES
dc.title Strategies for spectrum slicing based on restarted Lanczos methods es_ES
dc.type Artículo es_ES
dc.embargo.lift 10000-01-01
dc.embargo.terms forever es_ES
dc.identifier.doi 10.1007/s11075-012-9564-z
dc.relation.projectID info:eu-repo/grantAgreement/MICINN//TIN2009-07519/ES/Metodos Avanzados Y Tecnicas Computacionales Novedosas Para La Resolucion Numerica De Problemas De Valores Propios De Gran Dimension/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Sistemas Informáticos y Computación - Departament de Sistemes Informàtics i Computació es_ES
dc.description.bibliographicCitation Campos González, MC.; Román Moltó, JE. (2012). Strategies for spectrum slicing based on restarted Lanczos methods. Numerical Algorithms. 60(2):279-295. https://doi.org/10.1007/s11075-012-9564-z es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://link.springer.com/article/10.1007%2Fs11075-012-9564-z es_ES
dc.description.upvformatpinicio 279 es_ES
dc.description.upvformatpfin 295 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 60 es_ES
dc.description.issue 2 es_ES
dc.relation.senia 222627
dc.identifier.eissn 1572-9265
dc.contributor.funder Ministerio de Ciencia e Innovación es_ES
dc.description.references Amestoy, P.R, Duff, I.S., L’Excellent, J.Y.: Multifrontal parallel distributed symmetric and unsymmetric solvers. Comput. Methods Appl. Mech. Eng. 184(2–4), 501–520 (2000) es_ES
dc.description.references Balay, S., Brown, J., Buschelman, K., Eijkhout, V., Gropp, W., Kaushik, D., Knepley, M., McInnes, L.C., Smith, B., Zhang, H.: PETSc users manual. Tech. Rep. ANL-95/11 - Revision 3.2, Argonne National Laboratory (2011) es_ES
dc.description.references Ericsson, T., Ruhe, A.: The spectral transformation Lanczos method for the numerical solution of large sparse generalized symmetric eigenvalue problems. Math. Comput. 35(152), 1251–1268 (1980) es_ES
dc.description.references Grimes, R.G., Lewis, J.G., Simon, H.D.: A shifted block Lanczos algorithm for solving sparse symmetric generalized eigenproblems. SIAM J. Matrix Anal. Appl. 15(1), 228–272 (1994) es_ES
dc.description.references Hernandez, V., Roman, J.E., Vidal, V.: SLEPc: a scalable and flexible toolkit for the solution of eigenvalue problems. ACM Trans. Math. Softw. 31(3), 351–362 (2005) es_ES
dc.description.references Hernandez, V., Roman, J.E., Tomas, A.: Parallel Arnoldi eigensolvers with enhanced scalability via global communications rearrangement. Parallel Comput. 33(7–8), 521–540 (2007) es_ES
dc.description.references Marques, O.A.: BLZPACK: description and user’s guide. Tech. Rep. TR/PA/95/30, CERFACS, Toulouse, France (1995) es_ES
dc.description.references Meerbergen, K.: Changing poles in the rational Lanczos method for the Hermitian eigenvalue problem. Numer. Linear Algebra Appl. 8(1), 33–52 (2001) es_ES
dc.description.references Meerbergen, K., Scott, J.: The design of a block rational Lanczos code with partial reorthogonalization and implicit restarting. Tech. Rep. RAL-TR-2000-011, Rutherford Appleton Laboratory (2000) es_ES
dc.description.references Nour-Omid, B., Parlett, B.N., Ericsson, T., Jensen, P.S.: How to implement the spectral transformation. Math. Comput. 48(178), 663–673 (1987) es_ES
dc.description.references Olsson, K.H.A., Ruhe, A.: Rational Krylov for eigenvalue computation and model order reduction. BIT Numer. Math. 46, 99–111 (2006) es_ES
dc.description.references Ruhe, A.: Rational Krylov sequence methods for eigenvalue computation. Linear Algebra Appl. 58, 391–405 (1984) es_ES
dc.description.references Ruhe, A.: Rational Krylov subspace method. In: Bai, Z., Demmel, J., Dongarra, J., Ruhe, A., van der Vorst, H. (eds.) Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide, Society for Industrial and Applied Mathematics, pp. 246–249. Philadelphia (2000) es_ES
dc.description.references Sorensen, D.C.: Implicit application of polynomial filters in a k-step Arnoldi method. SIAM J. Matrix Anal. Appl. 13, 357–385 (1992) es_ES
dc.description.references Stewart, G.W.: A Krylov–Schur algorithm for large eigenproblems. SIAM J. Matrix Anal. Appl. 23(3), 601–614 (2001) es_ES
dc.description.references Vidal, AM., Garcia, V.M., Alonso, P., Bernabeu, M.O.: Parallel computation of the eigenvalues of symmetric Toeplitz matrices through iterative methods. J. Parallel Distrib. Comput. 68(8), 1113–1121 (2008) es_ES
dc.description.references Wu, K., Simon, H.: Thick-restart Lanczos method for large symmetric eigenvalue problems. SIAM J. Matrix Anal. Appl. 22(2), 602–616 (2000) es_ES
dc.description.references Zhang, H., Smith, B., Sternberg, M., Zapol, P.: SIPs: Shift-and-invert parallel spectral transformations. ACM Trans. Math. Softw. 33(2), 1–19 (2007) es_ES


Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro sencillo del ítem