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Papers by Delin Chu

Research paper thumbnail of Eigenvalue Embedding of Undamped Vibroacoustic Systems with No-spillover

SIAM Journal on Matrix Analysis and Applications, 2017

In this paper, we consider the eigenvalue embedding problem of the undamped vibroacoustic system ... more In this paper, we consider the eigenvalue embedding problem of the undamped vibroacoustic system with no-spillover (EEP-UVA), which is to update the original system to a new undamped vibroacoustic system, such that some eigen-structures are replaced with newly measured ones, while the remaining eigen-structures are kept unchanged. We provide a set of parametric solutions to the EEP-UVA. The freedoms in the parametric matrices can be further exploited to achieve some other desirable properties. The performance of the proposed algorithms are illustrated by numerical examples.

Research paper thumbnail of Correction to 'On the numerical computation in systems and control

IEEE Transactions on Automatic Control, 2003

Research paper thumbnail of SVD-Based Algorithms for the Best Rank-1 Approximation of a Symmetric Tensor

SIAM Journal on Matrix Analysis and Applications, 2018

Research paper thumbnail of Laser micromachining of through via interconnects in active die for 3D multichip module

Seventeenth IEEE/CPMT International Electronics Manufacturing Technology Symposium. 'Manufacturing Technologies - Present and Future'

Research paper thumbnail of Condition numbers and perturbation analysis for the Tikhonov regularization of discrete ill-posed problems

Numerical Linear Algebra with Applications, 2011

Research paper thumbnail of Inclusion Principle for Descriptor Systems

IEEE Transactions on Automatic Control, 2009

Research paper thumbnail of A Numerical Design of Interactors for General Descriptor Systems

IEEE Transactions on Automatic Control, 2012

Research paper thumbnail of Matrix Inequality Characterizations for Positive Realness of Descriptor Systems

In this talk, matrix inequality characterizations for the positive realness of descriptor systems... more In this talk, matrix inequality characterizations for the positive realness of descriptor systems are introduced. Hence, the celebrated positive real lemma for standard state space systems is established for descriptor systems. In addition, the lossless positive realness of both standard state space systems and descriptor systems are characterized explicitly based on the controllable staircase forms of standard state space systems and the generalized controllable staircase forms of descriptor systems, respectively. All are welcome THE UNIVERSITY OF HONG KONG

Research paper thumbnail of A Structure-Preserving Algorithm for Semi-Stabilizing Solutions of Generalized Algebraic Riccati Equations

In this paper, a structure-preserving algorithm is develop d for the computation of a semi-stabil... more In this paper, a structure-preserving algorithm is develop d for the computation of a semi-stabilizing solution of a Generalized Algebraic Riccati Equation (GARE ). The semi-stabilizing solution of GAREs has been used to characterize the solvability of the (J, J )-spectral factorization problem in control theory for gene ral rational matrices which may have poles and zeros on the extended imaginar y axis. The main difficulty in solving such a GARE lies in the fact that its associated Hamiltonian/skew-H amiltonian pencil has eigenvalues on the extended imaginary axis. Consequently, it is not clear which eigenspa ce of the associated Hamiltonian/skew-Hamiltonian pencil can characterize the desired semi-stabilizing solut ion. That is, it is not clear which eigenvectors and principa l vectors corresponding to the eigenvalues on the extended ima ginary axis should be contained in the eigenspace that we wish to compute. Hence, the well-known generalized ei genspace approach for the classi...

Research paper thumbnail of Reply to “Comment on ‘Separability of completely symmetric states in a multipartite system’ ”

The author of the Comment [Phys. Rev. A 104, 016401 (2021)] pointed out the missing part in the p... more The author of the Comment [Phys. Rev. A 104, 016401 (2021)] pointed out the missing part in the proof of Theorem 20 in our work [L. Qian et al., Phys. Rev. A 99, 032312 (2019)], and presented a sufficient and necessary condition for the separability of completely symmetric (CS) states in the two-qutrit system. While being technically correct, the proposed example is still a separable CS state according to Ha's sufficient and necessary condition. We provide another proof to show that every bipartite CS state of rank five is separable. This result bridges the gap appearing in our previous proof. It turns out that every two-qutrit CS state is separable, and thus making our conclusion (Theorem 20 of our work) still valid.

Research paper thumbnail of Methods for solving underdetermined systems

Numerical Linear Algebra with Applications

Research paper thumbnail of A Structure-Preserving Method for Positive Realness Problem in Control

Vietnam Journal of Mathematics

In this paper the positive realness problem in control theory is studied. A numerical method is d... more In this paper the positive realness problem in control theory is studied. A numerical method is developed for verifying the positive realness of a given proper rational matrix H(s) for which H(s) + HT(−s) has purely imaginary zeros. The proposed method is only based on orthogonal transformations, it is structure-preserving and has a complexity which is cubic in the state dimension of H(s). Some examples are given to illustrate the performance of the proposed method.

Research paper thumbnail of Least Squares Approximation via Sparse Subsampled Randomized Hadamard Transform

IEEE Transactions on Big Data

Research paper thumbnail of Separability of symmetric states and vandermonde decomposition

Research paper thumbnail of Sparse Uncorrelated Linear Discriminant Analysis for Undersampled Problems

IEEE Transactions on Neural Networks and Learning Systems

Research paper thumbnail of A Systematic Analysis on Analyticity of Semisimple Eigenvalues of Matrix-Valued Functions

SIAM Journal on Matrix Analysis and Applications

In this paper we study the existence of analytic eigenvalue functions of an analytic matrix-value... more In this paper we study the existence of analytic eigenvalue functions of an analytic matrix-valued function L(lambda,rho)L(\lambda,\rho)L(lambda,rho). Instead of proposing sufficient conditions for each individual case as in the literature, we propose a systematic scheme to discuss the existence of analytic eigenvalue functions of L(lambda,rho)L(\lambda,\rho)L(lambda,rho) when lambda_0\lambda_0lambda0 is a semisimple eigenvalue of L(lambda,0)L(\lambda,0)L(lambda,0). We show that lambda(rho)=lambda0+rhomu(rho)\lambda(\rho)=\lambda_0+\rho\mu(\rho)lambda(rho)=lambda0+rhomu(rho) is an eigenvalue of L(lambda,rho)L(\lambda,\rho)L(lambda,rho) if and only if mu(rho)\mu(\rho)mu(rho) is an eigenvalue of another analytic matrix-valued function P(mu,rho)P(\mu,\rho)P(mu,rho) which is constructed based on the first order (partial) derivatives of L(lambda,rho)L(\lambda,\rho)L(lambda,rho) at (lambda0,0)(\lambda_0,0)(lambda_0,0). Based on this result, a systematic scheme is proposed to check whether there exist analytic eigenvalue functions of L(lambda,rho)L(\lambda,\rho)L(lambda,rho). This systematic scheme covers existing sufficient conditions in the literature, and can lead to much more general conditions.

Research paper thumbnail of Nonconvex and Nonsmooth Optimization with Generalized Orthogonality Constraints: An Approximate Augmented Lagrangian Method

Journal of Scientific Computing, 2017

Nonconvex and nonsmooth optimization problems with linear equation and generalized orthogonality ... more Nonconvex and nonsmooth optimization problems with linear equation and generalized orthogonality constraints have wide applications. These problems are difficult to solve due to nonsmooth objective function and nonconvex constraints. In this paper, by introducing an extended proximal alternating linearized minimization (EPALM) method, we propose a framework based on the augmented Lagrangian scheme (EPALMAL). We also show that the EPALMAL method has global convergence in the sense that every bounded sequence generated by the EPALMAL method has at least one convergent subsequence that converges to the Karush–Kuhn–Tucker point of the original problem. Experiments on a variety of applications, including compressed modes and multivariate data analysis, have demonstrated that the proposed method is noticeably efficient and achieves comparable performance with existing methods.

Research paper thumbnail of Computing Singular Value Decompositions of Parameterized Matrices with Total Nonpositivity to High Relative Accuracy

Journal of Scientific Computing, 2016

In the last years, much effort has been devoted to high relative accuracy algorithms for the sing... more In the last years, much effort has been devoted to high relative accuracy algorithms for the singular value problem. However, such algorithms have been constructed only for a few classes of matrices with certain structure or properties. In this paper, we study a different class of matrices—parameterized matrices with total nonpositivity. We develop a new algorithm to compute singular value decompositions of such matrices to high relative accuracy. Our numerical results confirm the high relative accuracy of our algorithm.

Research paper thumbnail of Relative Perturbation Analysis for Eigenvalues and Singular Values of Totally Nonpositive Matrices

SIAM Journal on Matrix Analysis and Applications, 2015

Research paper thumbnail of Numerical Computation of the Fixed Poles in Disturbance Decoupling for Descriptor Systems

Lecture Notes in Electrical Engineering, 2011

ABSTRACT In this paper the algebraic characterizations for the fixed poles in the disturbance dec... more ABSTRACT In this paper the algebraic characterizations for the fixed poles in the disturbance decoupling problem for descriptor systems are derived. These algebraic characterizations lead to a numerically reliable algorithm for computing the fixed poles. The algorithm can be implemented directly using existing numerical linear algebra tools such as LAPACK and Matlab.

Research paper thumbnail of Eigenvalue Embedding of Undamped Vibroacoustic Systems with No-spillover

SIAM Journal on Matrix Analysis and Applications, 2017

In this paper, we consider the eigenvalue embedding problem of the undamped vibroacoustic system ... more In this paper, we consider the eigenvalue embedding problem of the undamped vibroacoustic system with no-spillover (EEP-UVA), which is to update the original system to a new undamped vibroacoustic system, such that some eigen-structures are replaced with newly measured ones, while the remaining eigen-structures are kept unchanged. We provide a set of parametric solutions to the EEP-UVA. The freedoms in the parametric matrices can be further exploited to achieve some other desirable properties. The performance of the proposed algorithms are illustrated by numerical examples.

Research paper thumbnail of Correction to 'On the numerical computation in systems and control

IEEE Transactions on Automatic Control, 2003

Research paper thumbnail of SVD-Based Algorithms for the Best Rank-1 Approximation of a Symmetric Tensor

SIAM Journal on Matrix Analysis and Applications, 2018

Research paper thumbnail of Laser micromachining of through via interconnects in active die for 3D multichip module

Seventeenth IEEE/CPMT International Electronics Manufacturing Technology Symposium. 'Manufacturing Technologies - Present and Future'

Research paper thumbnail of Condition numbers and perturbation analysis for the Tikhonov regularization of discrete ill-posed problems

Numerical Linear Algebra with Applications, 2011

Research paper thumbnail of Inclusion Principle for Descriptor Systems

IEEE Transactions on Automatic Control, 2009

Research paper thumbnail of A Numerical Design of Interactors for General Descriptor Systems

IEEE Transactions on Automatic Control, 2012

Research paper thumbnail of Matrix Inequality Characterizations for Positive Realness of Descriptor Systems

In this talk, matrix inequality characterizations for the positive realness of descriptor systems... more In this talk, matrix inequality characterizations for the positive realness of descriptor systems are introduced. Hence, the celebrated positive real lemma for standard state space systems is established for descriptor systems. In addition, the lossless positive realness of both standard state space systems and descriptor systems are characterized explicitly based on the controllable staircase forms of standard state space systems and the generalized controllable staircase forms of descriptor systems, respectively. All are welcome THE UNIVERSITY OF HONG KONG

Research paper thumbnail of A Structure-Preserving Algorithm for Semi-Stabilizing Solutions of Generalized Algebraic Riccati Equations

In this paper, a structure-preserving algorithm is develop d for the computation of a semi-stabil... more In this paper, a structure-preserving algorithm is develop d for the computation of a semi-stabilizing solution of a Generalized Algebraic Riccati Equation (GARE ). The semi-stabilizing solution of GAREs has been used to characterize the solvability of the (J, J )-spectral factorization problem in control theory for gene ral rational matrices which may have poles and zeros on the extended imaginar y axis. The main difficulty in solving such a GARE lies in the fact that its associated Hamiltonian/skew-H amiltonian pencil has eigenvalues on the extended imaginary axis. Consequently, it is not clear which eigenspa ce of the associated Hamiltonian/skew-Hamiltonian pencil can characterize the desired semi-stabilizing solut ion. That is, it is not clear which eigenvectors and principa l vectors corresponding to the eigenvalues on the extended ima ginary axis should be contained in the eigenspace that we wish to compute. Hence, the well-known generalized ei genspace approach for the classi...

Research paper thumbnail of Reply to “Comment on ‘Separability of completely symmetric states in a multipartite system’ ”

The author of the Comment [Phys. Rev. A 104, 016401 (2021)] pointed out the missing part in the p... more The author of the Comment [Phys. Rev. A 104, 016401 (2021)] pointed out the missing part in the proof of Theorem 20 in our work [L. Qian et al., Phys. Rev. A 99, 032312 (2019)], and presented a sufficient and necessary condition for the separability of completely symmetric (CS) states in the two-qutrit system. While being technically correct, the proposed example is still a separable CS state according to Ha's sufficient and necessary condition. We provide another proof to show that every bipartite CS state of rank five is separable. This result bridges the gap appearing in our previous proof. It turns out that every two-qutrit CS state is separable, and thus making our conclusion (Theorem 20 of our work) still valid.

Research paper thumbnail of Methods for solving underdetermined systems

Numerical Linear Algebra with Applications

Research paper thumbnail of A Structure-Preserving Method for Positive Realness Problem in Control

Vietnam Journal of Mathematics

In this paper the positive realness problem in control theory is studied. A numerical method is d... more In this paper the positive realness problem in control theory is studied. A numerical method is developed for verifying the positive realness of a given proper rational matrix H(s) for which H(s) + HT(−s) has purely imaginary zeros. The proposed method is only based on orthogonal transformations, it is structure-preserving and has a complexity which is cubic in the state dimension of H(s). Some examples are given to illustrate the performance of the proposed method.

Research paper thumbnail of Least Squares Approximation via Sparse Subsampled Randomized Hadamard Transform

IEEE Transactions on Big Data

Research paper thumbnail of Separability of symmetric states and vandermonde decomposition

Research paper thumbnail of Sparse Uncorrelated Linear Discriminant Analysis for Undersampled Problems

IEEE Transactions on Neural Networks and Learning Systems

Research paper thumbnail of A Systematic Analysis on Analyticity of Semisimple Eigenvalues of Matrix-Valued Functions

SIAM Journal on Matrix Analysis and Applications

In this paper we study the existence of analytic eigenvalue functions of an analytic matrix-value... more In this paper we study the existence of analytic eigenvalue functions of an analytic matrix-valued function L(lambda,rho)L(\lambda,\rho)L(lambda,rho). Instead of proposing sufficient conditions for each individual case as in the literature, we propose a systematic scheme to discuss the existence of analytic eigenvalue functions of L(lambda,rho)L(\lambda,\rho)L(lambda,rho) when lambda_0\lambda_0lambda0 is a semisimple eigenvalue of L(lambda,0)L(\lambda,0)L(lambda,0). We show that lambda(rho)=lambda0+rhomu(rho)\lambda(\rho)=\lambda_0+\rho\mu(\rho)lambda(rho)=lambda0+rhomu(rho) is an eigenvalue of L(lambda,rho)L(\lambda,\rho)L(lambda,rho) if and only if mu(rho)\mu(\rho)mu(rho) is an eigenvalue of another analytic matrix-valued function P(mu,rho)P(\mu,\rho)P(mu,rho) which is constructed based on the first order (partial) derivatives of L(lambda,rho)L(\lambda,\rho)L(lambda,rho) at (lambda0,0)(\lambda_0,0)(lambda_0,0). Based on this result, a systematic scheme is proposed to check whether there exist analytic eigenvalue functions of L(lambda,rho)L(\lambda,\rho)L(lambda,rho). This systematic scheme covers existing sufficient conditions in the literature, and can lead to much more general conditions.

Research paper thumbnail of Nonconvex and Nonsmooth Optimization with Generalized Orthogonality Constraints: An Approximate Augmented Lagrangian Method

Journal of Scientific Computing, 2017

Nonconvex and nonsmooth optimization problems with linear equation and generalized orthogonality ... more Nonconvex and nonsmooth optimization problems with linear equation and generalized orthogonality constraints have wide applications. These problems are difficult to solve due to nonsmooth objective function and nonconvex constraints. In this paper, by introducing an extended proximal alternating linearized minimization (EPALM) method, we propose a framework based on the augmented Lagrangian scheme (EPALMAL). We also show that the EPALMAL method has global convergence in the sense that every bounded sequence generated by the EPALMAL method has at least one convergent subsequence that converges to the Karush–Kuhn–Tucker point of the original problem. Experiments on a variety of applications, including compressed modes and multivariate data analysis, have demonstrated that the proposed method is noticeably efficient and achieves comparable performance with existing methods.

Research paper thumbnail of Computing Singular Value Decompositions of Parameterized Matrices with Total Nonpositivity to High Relative Accuracy

Journal of Scientific Computing, 2016

In the last years, much effort has been devoted to high relative accuracy algorithms for the sing... more In the last years, much effort has been devoted to high relative accuracy algorithms for the singular value problem. However, such algorithms have been constructed only for a few classes of matrices with certain structure or properties. In this paper, we study a different class of matrices—parameterized matrices with total nonpositivity. We develop a new algorithm to compute singular value decompositions of such matrices to high relative accuracy. Our numerical results confirm the high relative accuracy of our algorithm.

Research paper thumbnail of Relative Perturbation Analysis for Eigenvalues and Singular Values of Totally Nonpositive Matrices

SIAM Journal on Matrix Analysis and Applications, 2015

Research paper thumbnail of Numerical Computation of the Fixed Poles in Disturbance Decoupling for Descriptor Systems

Lecture Notes in Electrical Engineering, 2011

ABSTRACT In this paper the algebraic characterizations for the fixed poles in the disturbance dec... more ABSTRACT In this paper the algebraic characterizations for the fixed poles in the disturbance decoupling problem for descriptor systems are derived. These algebraic characterizations lead to a numerically reliable algorithm for computing the fixed poles. The algorithm can be implemented directly using existing numerical linear algebra tools such as LAPACK and Matlab.