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Restarted Q-Arnoldi-type methods exploiting symmetry in quadratic eigenvalue problems

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Restarted Q-Arnoldi-type methods exploiting symmetry in quadratic eigenvalue problems

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Campos, C.; Román Moltó, JE. (2016). Restarted Q-Arnoldi-type methods exploiting symmetry in quadratic eigenvalue problems. BIT Numerical Mathematics. 56(4):1213-1236. https://doi.org/10.1007/s10543-016-0601-5

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/81254

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Title: Restarted Q-Arnoldi-type methods exploiting symmetry in quadratic eigenvalue problems
Author: Campos, Carmen Román Moltó, José Enrique
UPV Unit: Universitat Politècnica de València. Departamento de Sistemas Informáticos y Computación - Departament de Sistemes Informàtics i Computació
Universitat Politècnica de València. Escola Tècnica Superior d'Enginyeria Informàtica
Issued date:
Abstract:
We investigate how to adapt the Q-Arnoldi method for the case of symmetric quadratic eigenvalue problems, that is, we are interested in computing a few eigenpairs of with M, C, K symmetric matrices. This problem has no ...[+]
Subjects: Quadratic eigenvalue problem , Pseudo-Lanczos , Q-Arnoldi , TOAR , Thick-restart , SLEPc
Copyrigths: Reserva de todos los derechos
Source:
BIT Numerical Mathematics. (issn: 0006-3835 )
DOI: 10.1007/s10543-016-0601-5
Publisher:
Springer Verlag (Germany)
Publisher version: https://link.springer.com/article/10.1007/s10543-016-0601-5
Project ID:
info:eu-repo/grantAgreement/MINECO//TIN2013-41049-P/ES/EXTENSION DE LA LIBRERIA SLEPC PARA POLINOMIOS MATRICIALES, FUNCIONES MATRICIALES Y ECUACIONES MATRICIALES EN PLATAFORMAS DE COMPUTACION EMERGENTES/
info:eu-repo/grantAgreement/MECD//AP2012-0608/ES/AP2012-0608/
Description: The final publication is available at Springer via http://dx.doi.org/ 10.1007/s10543-016-0601-5.
Thanks:
This work was supported by the Spanish Ministry of Economy and Competitiveness under Grant TIN2013-41049-P. Carmen Campos was supported by the Spanish Ministry of Education, Culture and Sport through an FPU Grant with ...[+]
Type: Artículo

References

Bai, Z., Su, Y.: SOAR: a second-order Arnoldi method for the solution of the quadratic eigenvalue problem. SIAM J. Matrix Anal. Appl. 26(3), 640–659 (2005)

Bai, Z., Day, D., Ye, Q.: ABLE: an adaptive block Lanczos method for non-Hermitian eigenvalue problems. SIAM J. Matrix Anal. Appl. 20(4), 1060–1082 (1999)

Bai, Z., Ericsson, T., Kowalski, T.: Symmetric indefinite Lanczos 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, pp. 249–260. Society for Industrial and Applied Mathematics, Philadelphia (2000) [+]
Bai, Z., Su, Y.: SOAR: a second-order Arnoldi method for the solution of the quadratic eigenvalue problem. SIAM J. Matrix Anal. Appl. 26(3), 640–659 (2005)

Bai, Z., Day, D., Ye, Q.: ABLE: an adaptive block Lanczos method for non-Hermitian eigenvalue problems. SIAM J. Matrix Anal. Appl. 20(4), 1060–1082 (1999)

Bai, Z., Ericsson, T., Kowalski, T.: Symmetric indefinite Lanczos 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, pp. 249–260. Society for Industrial and Applied Mathematics, Philadelphia (2000)

Balay, S., Abhyankar, S., Adams, M., Brown, J., Brune, P., Buschelman, K., Dalcin, L., Eijkhout, V., Gropp, W., Kaushik, D., Knepley, M., McInnes, L.C., Rupp, K., Smith, B., Zampini, S., Zhang, H.: PETSc users manual. Tech. Rep. ANL-95/11 - Revision 3.6, Argonne National Laboratory (2015)

Benner, P., Faßbender, H., Stoll, M.: Solving large-scale quadratic eigenvalue problems with Hamiltonian eigenstructure using a structure-preserving Krylov subspace method. Electron. Trans. Numer. Anal. 29, 212–229 (2008)

Betcke, T., Higham, N.J., Mehrmann, V., Schröder, C., Tisseur, F.: NLEVP: a collection of nonlinear eigenvalue problems. ACM Trans. Math. Softw. 39(2), 7:1–7:28 (2013)

Campos, C., Roman, J.E.: Parallel Krylov solvers for the polynomial eigenvalue problem in SLEPc (2015, submitted)

Day, D.: An efficient implementation of the nonsymmetric Lanczos algorithm. SIAM J. Matrix Anal. Appl. 18(3), 566–589 (1997)

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)

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)

Jia, Z., Sun, Y.: A refined variant of SHIRA for the skew-Hamiltonian/Hamiltonian (SHH) pencil eigenvalue problem. Taiwan J. Math. 17(1), 259–274 (2013)

Kressner, D., Roman, J.E.: Memory-efficient Arnoldi algorithms for linearizations of matrix polynomials in Chebyshev basis. Numer. Linear Algebra Appl. 21(4), 569–588 (2014)

Kressner, D., Pandur, M.M., Shao, M.: An indefinite variant of LOBPCG for definite matrix pencils. Numer. Algorithms 66(4), 681–703 (2014)

Lancaster, P.: Linearization of regular matrix polynomials. Electron. J. Linear Algebra 17, 21–27 (2008)

Lancaster, P., Ye, Q.: Rayleigh-Ritz and Lanczos methods for symmetric matrix pencils. Linear Algebra Appl. 185, 173–201 (1993)

Lu, D., Su, Y.: Two-level orthogonal Arnoldi process for the solution of quadratic eigenvalue problems (2012, manuscript)

Meerbergen, K.: The Lanczos method with semi-definite inner product. BIT 41(5), 1069–1078 (2001)

Meerbergen, K.: The Quadratic Arnoldi method for the solution of the quadratic eigenvalue problem. SIAM J. Matrix Anal. Appl. 30(4), 1463–1482 (2008)

Mehrmann, V., Watkins, D.: Structure-preserving methods for computing eigenpairs of large sparse skew-Hamiltonian/Hamiltonian pencils. SIAM J. Sci. Comput. 22(6), 1905–1925 (2001)

Parlett, B.N.: The symmetric Eigenvalue problem. Prentice-Hall, Englewood Cliffs (1980) (reissued with revisions by SIAM, Philadelphia)

Parlett, B.N., Chen, H.C.: Use of indefinite pencils for computing damped natural modes. Linear Algebra Appl. 140(1), 53–88 (1990)

Parlett, B.N., Taylor, D.R., Liu, Z.A.: A look-ahead Lánczos algorithm for unsymmetric matrices. Math. Comput. 44(169), 105–124 (1985)

de Samblanx, G., Bultheel, A.: Nested Lanczos: implicitly restarting an unsymmetric Lanczos algorithm. Numer. Algorithms 18(1), 31–50 (1998)

Sleijpen, G.L.G., Booten, A.G.L., Fokkema, D.R., van der Vorst, H.A.: Jacobi-Davidson type methods for generalized eigenproblems and polynomial eigenproblems. BIT 36(3), 595–633 (1996)

Stewart, G.W.: A Krylov-Schur algorithm for large eigenproblems. SIAM J. Matrix Anal. Appl. 23(3), 601–614 (2001)

Su, Y., Zhang, J., Bai, Z.: A compact Arnoldi algorithm for polynomial eigenvalue problems. In: Presented at RANMEP (2008)

Tisseur, F.: Tridiagonal-diagonal reduction of symmetric indefinite pairs. SIAM J. Matrix Anal. Appl. 26(1), 215–232 (2004)

Tisseur, F., Meerbergen, K.: The quadratic eigenvalue problem. SIAM Rev. 43(2), 235–286 (2001)

Watkins, D.S.: The matrix Eigenvalue problem: GR and Krylov subspace methods. Society for Industrial and Applied Mathematics (2007)

Wu, K., Simon, H.: Thick-restart Lanczos method for large symmetric eigenvalue problems. SIAM J. Matrix Anal. Appl. 22(2), 602–616 (2000)

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