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A Comparison of Factorization-Free Eigensolvers with Application to Cavity Resonators
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ACM Transactions on Mathematical Software (TOMS)
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Journal of Symbolic Computation
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A Jacobi-Davidson method for nonlinear and nonsymmetric eigenproblems
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IEEE Transactions on Pattern Analysis and Machine Intelligence
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Regularized Local Reconstruction for Clustering
PAKDD '09 Proceedings of the 13th Pacific-Asia Conference on Advances in Knowledge Discovery and Data Mining
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Journal of Computational and Applied Mathematics
Multilevel preconditioned iterative eigensolvers for Maxwell eigenvalue problems
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Journal of Computational and Applied Mathematics
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IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
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Journal of Computational and Applied Mathematics
PRIMME: preconditioned iterative multimethod eigensolver—methods and software description
ACM Transactions on Mathematical Software (TOMS)
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Journal of Computational Physics
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Journal of Computational Physics
Euro-Par'10 Proceedings of the 16th international Euro-Par conference on Parallel processing: Part II
SIAM Journal on Matrix Analysis and Applications
NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications
Towards a parallel multilevel preconditioned maxwell eigensolver
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
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Neural, Parallel & Scientific Computations
Low-rank quadratic semidefinite programming
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ACM Transactions on Mathematical Software (TOMS)
A Rayleigh-Ritz style method for large-scale discriminant analysis
Pattern Recognition
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Recently the Jacobi--Davidson subspace iteration method has been introduced as a new powerful technique for solving a variety of eigenproblems. In this paper we will further exploit this method and enhance it with several techniques so that practical and accurate algorithms are obtained. We will present two algorithms, JDQZ for the generalized eigenproblem and JDQR for the standard eigenproblem, that are based on the iterative construction of a (generalized) partial Schur form. The algorithms are suitable for the efficient computation of several (even multiple) eigenvalues and the corresponding eigenvectors near a user-specified target value in the complex plane. An attractive property of our algorithms is that explicit inversion of operators is avoided, which makes them potentially attractive for very large sparse matrix problems.We will show how effective restarts can be incorporated in the Jacobi--Davidson methods, very similar to the implicit restart procedure for the Arnoldi process. Then we will discuss the use of preconditioning, and, finally, we will illustrate the behavior of our algorithms by a number of well-chosen numerical experiments.