A Jacobi-Davidson method for computing partial generalized real Schur forms

T.L. Noorden, van; J. Rommes

doi:10.1007/978-3-540-34288-5_96

A Jacobi-Davidson method for computing partial generalized real Schur forms

T.L. Noorden, van, J. Rommes

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

In this paper, a new variant of the Jacobi-Davidson method is presented that is specifically designed for real unsymmetric matrix pencils. Whenever a pencil has a complex conjugated pair of eigenvalues, the method computes the two dimensional real invariant subspace spanned by the two corresponding complex conjugated eigenvectors. This is beneficial for memory costs and in many cases it also accelerates the convergence of the JD method. In numerical experiments, the RJDQZ variant is compared with the original JDQZ method.

Original language	English
Title of host publication	Numerical Mathematics and Advanced Applications (Proceedings 6th European Conference, Enumath2005, Santiago de Compostella, Spain, July 18-22, 2005)
Editors	A. Bermúdez de Castro, D. Gómez, P. Quintela, P. Salgado
Publisher	Springer
Pages	963-971
ISBN (Print)	3-540-34287-7
DOIs	https://doi.org/10.1007/978-3-540-34288-5_96
Publication status	Published - 2006

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10.1007/978-3-540-34288-5_96

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Noorden, van, T. L., & Rommes, J. (2006). A Jacobi-Davidson method for computing partial generalized real Schur forms. In A. Bermúdez de Castro, D. Gómez, P. Quintela, & P. Salgado (Eds.), Numerical Mathematics and Advanced Applications (Proceedings 6th European Conference, Enumath2005, Santiago de Compostella, Spain, July 18-22, 2005) (pp. 963-971). Springer. https://doi.org/10.1007/978-3-540-34288-5_96

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title = "A Jacobi-Davidson method for computing partial generalized real Schur forms",

abstract = "In this paper, a new variant of the Jacobi-Davidson method is presented that is specifically designed for real unsymmetric matrix pencils. Whenever a pencil has a complex conjugated pair of eigenvalues, the method computes the two dimensional real invariant subspace spanned by the two corresponding complex conjugated eigenvectors. This is beneficial for memory costs and in many cases it also accelerates the convergence of the JD method. In numerical experiments, the RJDQZ variant is compared with the original JDQZ method.",

author = "{Noorden, van}, T.L. and J. Rommes",

year = "2006",

doi = "10.1007/978-3-540-34288-5_96",

language = "English",

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editor = "{Berm{\'u}dez de Castro}, A. and D. G{\'o}mez and P. Quintela and P. Salgado",

booktitle = "Numerical Mathematics and Advanced Applications (Proceedings 6th European Conference, Enumath2005, Santiago de Compostella, Spain, July 18-22, 2005)",

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Noorden, van, TL & Rommes, J 2006, A Jacobi-Davidson method for computing partial generalized real Schur forms. in A Bermúdez de Castro, D Gómez, P Quintela & P Salgado (eds), Numerical Mathematics and Advanced Applications (Proceedings 6th European Conference, Enumath2005, Santiago de Compostella, Spain, July 18-22, 2005). Springer, pp. 963-971. https://doi.org/10.1007/978-3-540-34288-5_96

A Jacobi-Davidson method for computing partial generalized real Schur forms. / Noorden, van, T.L.; Rommes, J.

Numerical Mathematics and Advanced Applications (Proceedings 6th European Conference, Enumath2005, Santiago de Compostella, Spain, July 18-22, 2005). ed. / A. Bermúdez de Castro; D. Gómez; P. Quintela; P. Salgado. Springer, 2006. p. 963-971.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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N2 - In this paper, a new variant of the Jacobi-Davidson method is presented that is specifically designed for real unsymmetric matrix pencils. Whenever a pencil has a complex conjugated pair of eigenvalues, the method computes the two dimensional real invariant subspace spanned by the two corresponding complex conjugated eigenvectors. This is beneficial for memory costs and in many cases it also accelerates the convergence of the JD method. In numerical experiments, the RJDQZ variant is compared with the original JDQZ method.

AB - In this paper, a new variant of the Jacobi-Davidson method is presented that is specifically designed for real unsymmetric matrix pencils. Whenever a pencil has a complex conjugated pair of eigenvalues, the method computes the two dimensional real invariant subspace spanned by the two corresponding complex conjugated eigenvectors. This is beneficial for memory costs and in many cases it also accelerates the convergence of the JD method. In numerical experiments, the RJDQZ variant is compared with the original JDQZ method.

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EP - 971

BT - Numerical Mathematics and Advanced Applications (Proceedings 6th European Conference, Enumath2005, Santiago de Compostella, Spain, July 18-22, 2005)

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Noorden, van TL, Rommes J. A Jacobi-Davidson method for computing partial generalized real Schur forms. In Bermúdez de Castro A, Gómez D, Quintela P, Salgado P, editors, Numerical Mathematics and Advanced Applications (Proceedings 6th European Conference, Enumath2005, Santiago de Compostella, Spain, July 18-22, 2005). Springer. 2006. p. 963-971 https://doi.org/10.1007/978-3-540-34288-5_96

A Jacobi-Davidson method for computing partial generalized real Schur forms

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