Volume 7, Issue 1
Implicitly Restarted Refined Partially Orthogonal Projection Method with Deflation

Wei Wei & Hua Dai

East Asian J. Appl. Math., 7 (2017), pp. 1-20.

Published online: 2018-02

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  • Abstract

In this paper we consider the computation of some eigenpairs with smallest eigenvalues in modulus of large-scale polynomial eigenvalue problem. Recently, a partially orthogonal projection method and its refinement scheme were presented for solving the polynomial eigenvalue problem. The methods preserve the structures and properties of the original polynomial eigenvalue problem. Implicitly updating the starting vector and constructing better projection subspace, we develop an implicitly restarted version of the partially orthogonal projection method. Combining the implicit restarting strategy with the refinement scheme, we present an implicitly restarted refined partially orthogonal projection method. In order to avoid the situation that the converged eigenvalues converge repeatedly in the later iterations, we propose a novel explicit non-equivalence low-rank deflation technique. Finally some numerical experiments show that the implicitly restarted refined partially orthogonal projection method with the explicit non-equivalence low-rank deflation technique is efficient and robust.

  • Keywords

Polynomial eigenvalue problem, partially orthogonal projection method, refinement, implicitly restarting, non-equivalence low-rank deflation.

  • AMS Subject Headings

65F15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-7-1, author = {}, title = {Implicitly Restarted Refined Partially Orthogonal Projection Method with Deflation}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {7}, number = {1}, pages = {1--20}, abstract = {

In this paper we consider the computation of some eigenpairs with smallest eigenvalues in modulus of large-scale polynomial eigenvalue problem. Recently, a partially orthogonal projection method and its refinement scheme were presented for solving the polynomial eigenvalue problem. The methods preserve the structures and properties of the original polynomial eigenvalue problem. Implicitly updating the starting vector and constructing better projection subspace, we develop an implicitly restarted version of the partially orthogonal projection method. Combining the implicit restarting strategy with the refinement scheme, we present an implicitly restarted refined partially orthogonal projection method. In order to avoid the situation that the converged eigenvalues converge repeatedly in the later iterations, we propose a novel explicit non-equivalence low-rank deflation technique. Finally some numerical experiments show that the implicitly restarted refined partially orthogonal projection method with the explicit non-equivalence low-rank deflation technique is efficient and robust.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.070816.131016a}, url = {http://global-sci.org/intro/article_detail/eajam/10731.html} }
TY - JOUR T1 - Implicitly Restarted Refined Partially Orthogonal Projection Method with Deflation JO - East Asian Journal on Applied Mathematics VL - 1 SP - 1 EP - 20 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.070816.131016a UR - https://global-sci.org/intro/article_detail/eajam/10731.html KW - Polynomial eigenvalue problem, partially orthogonal projection method, refinement, implicitly restarting, non-equivalence low-rank deflation. AB -

In this paper we consider the computation of some eigenpairs with smallest eigenvalues in modulus of large-scale polynomial eigenvalue problem. Recently, a partially orthogonal projection method and its refinement scheme were presented for solving the polynomial eigenvalue problem. The methods preserve the structures and properties of the original polynomial eigenvalue problem. Implicitly updating the starting vector and constructing better projection subspace, we develop an implicitly restarted version of the partially orthogonal projection method. Combining the implicit restarting strategy with the refinement scheme, we present an implicitly restarted refined partially orthogonal projection method. In order to avoid the situation that the converged eigenvalues converge repeatedly in the later iterations, we propose a novel explicit non-equivalence low-rank deflation technique. Finally some numerical experiments show that the implicitly restarted refined partially orthogonal projection method with the explicit non-equivalence low-rank deflation technique is efficient and robust.

Wei Wei & Hua Dai. (2020). Implicitly Restarted Refined Partially Orthogonal Projection Method with Deflation. East Asian Journal on Applied Mathematics. 7 (1). 1-20. doi:10.4208/eajam.070816.131016a
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