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Hamiltonian Square Roots of SkewHamiltonian Matrices
, 1997
"... We present a constructive existence proof that every real skewHamiltonian matrix W has a real Hamiltonian square root. The key step in this construction shows how one may bring any such W into a real quasiJordan canonical form via symplectic similarity. We show further that every W has infinitely ..."
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Cited by 28 (10 self)
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We present a constructive existence proof that every real skewHamiltonian matrix W has a real Hamiltonian square root. The key step in this construction shows how one may bring any such W into a real quasiJordan canonical form via symplectic similarity. We show further that every W has
The Solvability Conditions for the Inverse Eigenvalue Problem of Hermitian and Generalized SkewHamiltonian Matrices and Its Approximation
"... In this paper, we first consider the inverse eigenvalue problem as follows: Find a matrix A with specified eigenpairs, where A is a Hermitian and generalized skewHamiltonian matrix. The sufficient and necessary conditions are obtained, and a general representation of such a matrix is presented. We ..."
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In this paper, we first consider the inverse eigenvalue problem as follows: Find a matrix A with specified eigenpairs, where A is a Hermitian and generalized skewHamiltonian matrix. The sufficient and necessary conditions are obtained, and a general representation of such a matrix is presented
A Note on the Numerical Solution of Complex Hamiltonian and SkewHamiltonian Eigenvalue Problems
 Electr. Trans. Num. Anal
, 1999
"... In this paper we describe a simple observation that can be used to extend two recently proposed structure preserving methods for the eigenvalue problem for real Hamiltonian matrices to the case of complex Hamiltonian and skewHamiltonian matrices. Key words. eigenvalue problem, Hamiltonian matrix, ..."
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Cited by 24 (16 self)
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In this paper we describe a simple observation that can be used to extend two recently proposed structure preserving methods for the eigenvalue problem for real Hamiltonian matrices to the case of complex Hamiltonian and skewHamiltonian matrices. Key words. eigenvalue problem, Hamiltonian matrix
A NOTE ON THE NUMERICAL SOLUTION OF COMPLEX HAMILTONIAN AND SKEWHAMILTONIAN EIGENVALUE PROBLEMS∗
"... Abstract. In this paper we describe a simple observation that can be used to extend two recently proposed structure preserving methods for the eigenvalue problem for real Hamiltonian matrices to the case of complex Hamiltonian and skewHamiltonian matrices. ..."
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Abstract. In this paper we describe a simple observation that can be used to extend two recently proposed structure preserving methods for the eigenvalue problem for real Hamiltonian matrices to the case of complex Hamiltonian and skewHamiltonian matrices.
SkewHamiltonian and Hamiltonian eigenvalue problems: Theory, algorithms and applications
 Proceedings of ApplMath03, Brijuni (Croatia
"... SkewHamiltonian and Hamiltonian eigenvalue problems arise from a number of applications, particularly in systems and control theory. The preservation of the underlying matrix structures often plays an important role in these applications and may lead to more accurate and more efficient computation ..."
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Cited by 16 (6 self)
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SkewHamiltonian and Hamiltonian eigenvalue problems arise from a number of applications, particularly in systems and control theory. The preservation of the underlying matrix structures often plays an important role in these applications and may lead to more accurate and more efficient
A Note on the Numerical Solution of Complex Hamiltonian and SkewHamiltonian Eigenvalue Problems
 Electr. Trans. Num. Anal
, 1998
"... In this paper we describe a simple observation that can be used to extend two recently proposed structure preserving methods for the eigenvalue problem for real Hamiltonian matrices to the case of complex Hamiltonian and skewHamiltonian matrices. Keywords. Eigenvalue problem, Hamiltonian matrix, s ..."
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In this paper we describe a simple observation that can be used to extend two recently proposed structure preserving methods for the eigenvalue problem for real Hamiltonian matrices to the case of complex Hamiltonian and skewHamiltonian matrices. Keywords. Eigenvalue problem, Hamiltonian matrix
Nonlinear component analysis as a kernel eigenvalue problem

, 1996
"... We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map; for instance the space of all ..."
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Cited by 1554 (85 self)
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We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map; for instance the space of all
Perturbation bounds for isotropic invariant subspaces of skewHamiltonian matrices
 SIAM J. Matrix Anal. Appl
"... Abstract. We investigate the behavior of isotropic invariant subspaces of skewHamiltonian matrices under structured perturbations. It is shown that finding a nearby subspace is equivalent to solving a certain quadratic matrix equation. This connection is used to derive meaningful error bounds and c ..."
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Cited by 6 (4 self)
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Abstract. We investigate the behavior of isotropic invariant subspaces of skewHamiltonian matrices under structured perturbations. It is shown that finding a nearby subspace is equivalent to solving a certain quadratic matrix equation. This connection is used to derive meaningful error bounds
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
, 2008
"... ..."
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
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Cited by 1231 (13 self)
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the solution to a nonlinear programming relaxation. This relaxation can be interpreted both as a semidefinite program and as an eigenvalue minimization problem. The best previously known approximation algorithms for these problems had performance guarantees of ...
Results 1  10
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