Delin Chu - Profile on Academia.edu (original) (raw)

Papers by Delin Chu

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.

IEEE Transactions on Automatic Control, 2003

SIAM Journal on Matrix Analysis and Applications, 2018

This paper revisits the problem of finding the best rank-1 approximation to a symmetric tensor an... more This paper revisits the problem of finding the best rank-1 approximation to a symmetric tensor and makes three contributions. First, in contrast to the many long and lingering arguments in the literature, it offers a straightforward justification that generically the best rank-1 approximation to a symmetric tensor is symmetric. Second, in contrast to the typical workhorse in the practice for the low-rank tensor approximation, namely, the alternating least squares (ALS) technique which improves one factor a time, this paper proposes three alternative algorithms, based on the singular value decomposition (SVD) that modifies two factors a time. One step of SVD-based iteration is superior to two steps of ALS iterations. Third, it is proved that not only the generalized Rayleigh quotients generated from the three SVD-based algorithms enjoy monotone convergence, but also that the iterates themselves converge.

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

One method to increase density in integrated circuits (iC) is to stack die to create a 3-0 multic... more One method to increase density in integrated circuits (iC) is to stack die to create a 3-0 multichip module (MCM). In the past, special post wafer processing was done to bring interconnects out to the edge of the die. The die were sawed, glued, and stacked. Special processing was done to create interconnects on the edge to provide for interconnects to each of the die. These processes require an IC type fabrication facility @ab) and special processing equipment. It contrast, we have developed packaging assembly methods to created vertical through vias in bondpads of active silicon die, isolate these vias, and metal fill these vias without the use of a special IC fab. These die with through vias can then be joined and stacked to create a 3-0 MCM. Vertical through vias in active die are created by laser micromachining using a Nd:YAG laser. Besides the fundamental 1064 nm (infia-red) laser wavelength of a Nd:YAG laser, modifcations to our Nd:YAG laser allowed us to generate the second harmonic 532 nm (green) laser wavelength and fourth harmonic 266nm (ultra violet) laser wavelength in laser micromachining for these vias. Experiments were conducted to determine the best laser wavelengths to use for laser micromachining of vertical through vias in order to minimize damage to the active die. Via isolation experiments were done in order determine the best method in isolating the bondpads of the die. Die thinning techniques were developed to allow for die thickness as thin as 50 pm. This would allow for high 3-0 density when the die are stacked. A method was developed to metal fill the vias with solder using a wire bonder with solder wire.

Numerical Linear Algebra with Applications, 2011

One of the most successful methods for solving the least-squares problem min x Ax −b 2 with a hig... more One of the most successful methods for solving the least-squares problem min x Ax −b 2 with a highly ill-conditioned or rank deficient coefficient matrix A is the method of Tikhonov regularization. In this paper, we derive the normwise, mixed and componentwise condition numbers and componentwise perturbation bounds for the Tikhonov regularization. Our results are sharper than the known results. Some numerical examples are given to illustrate our results.

IEEE Transactions on Automatic Control, 2009

The purpose of this paper is to propose an expansion-contraction framework for linear constant de... more The purpose of this paper is to propose an expansion-contraction framework for linear constant descriptor systems within the inclusion principle for dynamic systems. Our primary objective is to provide an explicit characterization of the expansion process whereby a given descriptor system is expanded into the larger space where all its solutions are reproducible by the expanded descriptor system if appropriate initial conditions are selected. When a control law is formulated in the expanded space, the proposed characterizations provide contractibility conditions for implementation of the control law in the original system. A full freedom is provided for selecting appropriate matrices in the proposed expansion-contraction control scheme. In particular, the derived theoretical framework serves as a flexible environment for expansion-contraction control design of descriptor systems under overlapping information structure constraints.

IEEE Transactions on Automatic Control, 2012

In this technical note, we develop a numerically reliable method to design an interactor for a ge... more In this technical note, we develop a numerically reliable method to design an interactor for a general descriptor system relative to a stability region C and an offending zero set. Our main result is based on a condensed form. This condensed form is independent of the offending zeros , and is computed using only orthogonal transformations and hence is numerically backward stable.

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...

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.

Methods for solving underdetermined systems

Numerical Linear Algebra with Applications

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.

Least Squares Approximation via Sparse Subsampled Randomized Hadamard Transform

IEEE Transactions on Big Data

New Journal of Physics

Symmetry is one of the central mysteries of quantum mechanics and plays an essential role in mult... more Symmetry is one of the central mysteries of quantum mechanics and plays an essential role in multipartite entanglement. In this paper, we consider the separability problem of quantum states in the symmetric space. We establish the relation between the separability of multiqubit symmetric states and the decomposability of Hermitian positive semidefinite matrices. This relation allows us to exchange concepts and ideas between quantum entanglement and Vandermonde decomposition. As an application, we build a suite of tools to investigate the decomposability and show the power of this relation both in theoretical and numerical aspects. For theoretical results, we establish the witness for the decomposability similar to the entanglement witness and characterize the decomposability of some subclasses of matrices. Furthermore, we provide the necessary conditions for the decomposability. Besides, we suggest a numerical algorithm to check whether a given matrix is decomposable. The numerical examples are tested to show the effectiveness.

IEEE Transactions on Neural Networks and Learning Systems

In this paper, we develop a novel approach for sparse uncorrelated linear discriminant analysis (... more In this paper, we develop a novel approach for sparse uncorrelated linear discriminant analysis (ULDA). Our proposal is based on characterization of all solutions of the generalized ULDA. We incorporate sparsity into the ULDA transformation by seeking the solution with minimum 1-norm from all minimum dimension solutions of the generalized ULDA. The problem is then formulated as a 1-minimization problem and is solved by accelerated linearized Bregman method. Experiments on high-dimensional gene expression data demonstrate that our approach not only computes extremely sparse solutions but also performs well in classification. Experimental results also show that our approach can help for data visualization in lowdimensional space.

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.

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.

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.

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

SIAM Journal on Matrix Analysis and Applications, 2015

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.

Well-posedness of two classes of singular distributed parameter systems in Hilbert space

2010 11th International Conference on Control Automation Robotics & Vision, 2010

ABSTRACT One of the most important problems for the study of singular distributed parameter syste... more ABSTRACT One of the most important problems for the study of singular distributed parameter systems is the well-posedness. Not only is it very important for the study of stability of singular distributed parameter systems, but also it is the theoretic basis for the study of the related problem of optimal control. In this paper, the concepts and the properties of generalized operator semigroup(GOS) and generalized integral semigroup(GIS) are given in Hilbert space, the solving problem of the non-homogeneous singular distributed parameter system is discussed by the concepts and the properties of GOS and GIS in Hilbert space, and some important results of the two classes of singular distributed parameter systems are given.

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.

IEEE Transactions on Automatic Control, 2003

SIAM Journal on Matrix Analysis and Applications, 2018

This paper revisits the problem of finding the best rank-1 approximation to a symmetric tensor an... more This paper revisits the problem of finding the best rank-1 approximation to a symmetric tensor and makes three contributions. First, in contrast to the many long and lingering arguments in the literature, it offers a straightforward justification that generically the best rank-1 approximation to a symmetric tensor is symmetric. Second, in contrast to the typical workhorse in the practice for the low-rank tensor approximation, namely, the alternating least squares (ALS) technique which improves one factor a time, this paper proposes three alternative algorithms, based on the singular value decomposition (SVD) that modifies two factors a time. One step of SVD-based iteration is superior to two steps of ALS iterations. Third, it is proved that not only the generalized Rayleigh quotients generated from the three SVD-based algorithms enjoy monotone convergence, but also that the iterates themselves converge.

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

One method to increase density in integrated circuits (iC) is to stack die to create a 3-0 multic... more One method to increase density in integrated circuits (iC) is to stack die to create a 3-0 multichip module (MCM). In the past, special post wafer processing was done to bring interconnects out to the edge of the die. The die were sawed, glued, and stacked. Special processing was done to create interconnects on the edge to provide for interconnects to each of the die. These processes require an IC type fabrication facility @ab) and special processing equipment. It contrast, we have developed packaging assembly methods to created vertical through vias in bondpads of active silicon die, isolate these vias, and metal fill these vias without the use of a special IC fab. These die with through vias can then be joined and stacked to create a 3-0 MCM. Vertical through vias in active die are created by laser micromachining using a Nd:YAG laser. Besides the fundamental 1064 nm (infia-red) laser wavelength of a Nd:YAG laser, modifcations to our Nd:YAG laser allowed us to generate the second harmonic 532 nm (green) laser wavelength and fourth harmonic 266nm (ultra violet) laser wavelength in laser micromachining for these vias. Experiments were conducted to determine the best laser wavelengths to use for laser micromachining of vertical through vias in order to minimize damage to the active die. Via isolation experiments were done in order determine the best method in isolating the bondpads of the die. Die thinning techniques were developed to allow for die thickness as thin as 50 pm. This would allow for high 3-0 density when the die are stacked. A method was developed to metal fill the vias with solder using a wire bonder with solder wire.

Numerical Linear Algebra with Applications, 2011

One of the most successful methods for solving the least-squares problem min x Ax −b 2 with a hig... more One of the most successful methods for solving the least-squares problem min x Ax −b 2 with a highly ill-conditioned or rank deficient coefficient matrix A is the method of Tikhonov regularization. In this paper, we derive the normwise, mixed and componentwise condition numbers and componentwise perturbation bounds for the Tikhonov regularization. Our results are sharper than the known results. Some numerical examples are given to illustrate our results.

IEEE Transactions on Automatic Control, 2009

The purpose of this paper is to propose an expansion-contraction framework for linear constant de... more The purpose of this paper is to propose an expansion-contraction framework for linear constant descriptor systems within the inclusion principle for dynamic systems. Our primary objective is to provide an explicit characterization of the expansion process whereby a given descriptor system is expanded into the larger space where all its solutions are reproducible by the expanded descriptor system if appropriate initial conditions are selected. When a control law is formulated in the expanded space, the proposed characterizations provide contractibility conditions for implementation of the control law in the original system. A full freedom is provided for selecting appropriate matrices in the proposed expansion-contraction control scheme. In particular, the derived theoretical framework serves as a flexible environment for expansion-contraction control design of descriptor systems under overlapping information structure constraints.

IEEE Transactions on Automatic Control, 2012

In this technical note, we develop a numerically reliable method to design an interactor for a ge... more In this technical note, we develop a numerically reliable method to design an interactor for a general descriptor system relative to a stability region C and an offending zero set. Our main result is based on a condensed form. This condensed form is independent of the offending zeros , and is computed using only orthogonal transformations and hence is numerically backward stable.

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...

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.

Methods for solving underdetermined systems

Numerical Linear Algebra with Applications

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.

Least Squares Approximation via Sparse Subsampled Randomized Hadamard Transform

IEEE Transactions on Big Data

New Journal of Physics

Symmetry is one of the central mysteries of quantum mechanics and plays an essential role in mult... more Symmetry is one of the central mysteries of quantum mechanics and plays an essential role in multipartite entanglement. In this paper, we consider the separability problem of quantum states in the symmetric space. We establish the relation between the separability of multiqubit symmetric states and the decomposability of Hermitian positive semidefinite matrices. This relation allows us to exchange concepts and ideas between quantum entanglement and Vandermonde decomposition. As an application, we build a suite of tools to investigate the decomposability and show the power of this relation both in theoretical and numerical aspects. For theoretical results, we establish the witness for the decomposability similar to the entanglement witness and characterize the decomposability of some subclasses of matrices. Furthermore, we provide the necessary conditions for the decomposability. Besides, we suggest a numerical algorithm to check whether a given matrix is decomposable. The numerical examples are tested to show the effectiveness.

IEEE Transactions on Neural Networks and Learning Systems

In this paper, we develop a novel approach for sparse uncorrelated linear discriminant analysis (... more In this paper, we develop a novel approach for sparse uncorrelated linear discriminant analysis (ULDA). Our proposal is based on characterization of all solutions of the generalized ULDA. We incorporate sparsity into the ULDA transformation by seeking the solution with minimum 1-norm from all minimum dimension solutions of the generalized ULDA. The problem is then formulated as a 1-minimization problem and is solved by accelerated linearized Bregman method. Experiments on high-dimensional gene expression data demonstrate that our approach not only computes extremely sparse solutions but also performs well in classification. Experimental results also show that our approach can help for data visualization in lowdimensional space.

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.

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.

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.

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

SIAM Journal on Matrix Analysis and Applications, 2015

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.

Well-posedness of two classes of singular distributed parameter systems in Hilbert space

2010 11th International Conference on Control Automation Robotics & Vision, 2010

ABSTRACT One of the most important problems for the study of singular distributed parameter syste... more ABSTRACT One of the most important problems for the study of singular distributed parameter systems is the well-posedness. Not only is it very important for the study of stability of singular distributed parameter systems, but also it is the theoretic basis for the study of the related problem of optimal control. In this paper, the concepts and the properties of generalized operator semigroup(GOS) and generalized integral semigroup(GIS) are given in Hilbert space, the solving problem of the non-homogeneous singular distributed parameter system is discussed by the concepts and the properties of GOS and GIS in Hilbert space, and some important results of the two classes of singular distributed parameter systems are given.