Solving Eigenvalue problem as an optimization problem on Manifold
Pages 357 - 358
Abstract
We want to solve the generalized eigenvalue problem by posing it as an optimization problem on manifold. It is based on a constrained truncated-GMRES [8] trust-region strategy to optimize the Rayleigh quotient, in the framework of a recently-proposed trust-region scheme on Riemannian manifolds [1--5].
References
[1]
PA Absil, Christopher Baker, and Kyle Gallivan. 2006. A truncated-CG style method for symmetric generalized eigenvalue problems. J. Comput. Appl. Math. 189 (05 2006), 274--285. https://doi.org/10.1016/j.cam.2005.10.006
[2]
P.-A. Absil, C.G. Baker, and K.A. Gallivan. 2007. Trust-Region Methods on Riemannian Manifolds. Foundations of Computational Mathematics 7, 3 (01 Jul 2007), 303--330.
[3]
P. A. Absil, C. G. Baker, K. A. Gallivan, and A. Sameh. 2005. Adaptive Model Trust Region Methods for Generalized Eigenvalue Problems. In Computational Science -- ICCS 2005, Vaidy S. Sunderam, Geert Dick van Albada, Peter M. A. Sloot, and Jack J. Dongarra (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 33--41.
[4]
P.-A. Absil, R. Mahony, and R. Sepulchre. 2008. Optimization Algorithms on Matrix Manifolds. Princeton University Press, Princeton, NJ.
[5]
C. G. Baker, P. A. Absil, and K. A. Gallivan. 2006. An Implicit Riemannian Trust-Region Method for the Symmetric Generalized Eigenproblem. In Computational Science -- ICCS 2006, Vassil N. Alexandrov, Geert Dick van Albada, Peter M. A. Sloot, and Jack Dongarra (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 210--217.
[6]
Alan. Edelman, Tomás A. Arias, and Steven T. Smith. 1998. The Geometry of Algorithms with Orthogonality Constraints. SIAM J. Matrix Anal. Appl. 20, 2 (1998), 303--353.
[7]
Yvan Notay. 2002. Combination of Jacobi-Davidson and conjugate gradients for the partial symmetric eigenproblem. Numerical Lin. Alg. with Applic. 9 (2002), 21--44.
[8]
Youcef Saad and Kesheng Wu. 1994. DQGMRES: a Quasi - minimal residual algorithm based on incomplete orthogonalization. (05 1994).
[9]
Gerard L. G. Sleijpen and Henk A. Van der. 2000. A Jacobi--Davidson Iteration Method for Linear Eigenvalue Problems. SIAM Rev. 42, 2 (June 2000), 267--293.
[10]
Trond. Steihaug. 1983. The Conjugate Gradient Method and Trust Regions in Large Scale Optimization. SIAM J. Numer. Anal. 20, 3 (1983), 626--637.
- Solving Eigenvalue problem as an optimization problem on Manifold
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Published In
January 2020
399 pages
ISBN:9781450377386
DOI:10.1145/3371158
- General Chairs:
- Vasudeva Varma,
- Subbarao Kambhampati,
- Program Chairs:
- Arnab Bhattacharya,
- Sriraam Natarajan,
- Publications Chair:
- Rishiraj Saha Roy
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Published: 15 January 2020
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