Dr Delin Chu

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Department of Mathematics

National University of Singapore

Singapore

Email: matchudl@nus.edu.sg

Tel: 65-65166912

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Editorial boards:

Automatica-Elsevier, 2008--

Journal of Computational and Applied Mathematics-Elsevier, May 2011--

## Research

Major Area of Research:

Numerical Linear Algebra and Its Applications

Research Interests

Numerical Linear Algebra and Its Applications,

Matrix Theory and Computations,

Scientific Computing and Numerical Analysis.

Selected Publication:

[1] H. Zhu, X.W. Zhang, Delin Chu, and L. Liao. Nonconvex and nonsmooth optimization with generalized orthogonality constraints: An approximate augmented Lagrangian method, Journal of Scientific Computing, 72, No. 1 (2017):331-372.

[2] R. Huang and Delin Chu. Computing singular value decompositions of parameterized matrices with total nonpositivity to high relative accuracy, Journal of Scientific Computing, 71, No. 2 (2017):682-711.

[3] J. Qian, Delin Chu, R. C.E. Tan.  A systematic analysis on analyticity of semisimple eigenvalues of matrix-valued functions, SIAM Journal on Matrix Analysis and Applications,  37, No. 4 (2016):1581-1599.

[4] X.W. Zhang, {Delin Chu}, and R. C.E. Tan. Sparse uncorrelated linear discriminant analysis for undersampled problems, IEEE Transactions on Neural Networks and Learning Systems, 27, No.7 (2016):1469--1485.

[5] X. W. Zhang, L. Cheng, Delin Chu, L. Liao, M. Ng and R. C.E. Tan. Incremental regularized least Squares for dimensionality reduction of large-scale data.

SIAM Journal on Scientific Computing, 38, No.3 (2016):B414--B439.

[6] J. Qian, Delin Chu, R. C.E. Tan. Analyticity of semisimple eigenvalues and corresponding eigenvectors of matrix-valued functions, SIAM Journal on Matrix Analysis and Applications,  36, No.4 (2015):1542--1566.

[7] Delin Chu, L. Liao, M. Ng and X.Y.Wang.  Incremental linear discriminant analysis: A new algorithm and comparisons, IEEE Transactions on Neural Networks and Learning Systems, 26, No.11 (2015):2716--2735.

[8] R. Huang and Delin Chu.  Relative perturbation analysis for eigenvalues and singular values of totally nonpositive matrices. SIAM Journal on Matrix Analysis and Applications,  36, No.2 (2015):476--495.

[9] T. Li and Delin Chu, A structure-preserving algorithm for semi-stabilizing solutions of generalized algebraic Riccati equations. Electronic Transactions on Numerical Analysis, 41 (2014):396--419.

[10] Q.H. Chen, Delin Chu and R. C. E. Tan, Double obstacle control problem for quasilinear elliptic variational inequality with source term, Nonlinear Analysis: Real World Applications, 18 (2014):108--120.

[11] Delin Chu, L. Liao, M. Ng and X.W. Zhang. Sparse canonical correlation analysis: New formulation and algorithm, IEEE Transactions on Pattern Analysis and Machine Intelligence,

35, No.12 (2013):3050-3065.

[12] J. Yang, Delin Chu, L. Zhang, Y. Xu and J.Yu Yang. Sparse representation classifier steered discriminative projection with applications to face recognition, IEEE Transactions on Neural Networks and Learning Systems, 24, No. 7 (2013):1023-1035.

[13] J. Qian, A. L. Andrew, Delin Chu, and R. C.E. Tan. Computing derivatives of repeated eigenvalues and corresponding eigenvectors of quadratic eigenvalue problems. SIAM Journal on Matrix Analysis and Applications, 34, No.3 (2013):1089--1111.

[14] Delin Chu, L. Liao and M. Ng. Sparse orthogonal linear discriminant analysis, SIAM Journal on Scientific Computing, 34, No.5 (2012):A2421--A2443.

[15] Delin Chu, and Y.S. Hung. A numerical design of interactors for general descriptor systems,

IEEE Transactions on Automatic Control, 57, No.9 (2012):2396--2399.

[16] W. Ching, Delin Chu, L. Liao and X. Wang.  Regularized orthogonal linear discriminant analysis, Pattern Recognition, 45, No.7 (2012):2719--2732.

[17] Delin Chu, Goh Siong Thye and Y.S. Hung. Characterization of all solutions for undersampled uncorrelated linear discriminant analysis problems. SIAM Journal on Matrix Analysis and Applications, 32, No.3 (2011):820--844.

[18] Q.H. Chen, Delin Chu and R. C. E. Tan, Pontryagin's principle for state-constrained evolutionary differential complementarity system. Nonlinear Analysis: Real World Applications, 12, No.3 (2011):1459--1474.

[19] Delin Chu, L. Lin, R. C. E. Tan and Y. Wei. Condition numbers and perturbation analysis for Tikhonov regularization of discrete ill-posed problems. Numerical Linear Algebra with Applications, 18, No.1 (2011):87–-103.

[20] Delin Chu and  Goh Siong Thye. A new and fast orthogonal linear discriminant analysis on undersampled problems. SIAM Journal on Scientific Computing.  32, No.4 (2010):2274-2297.

[21] Delin Chu and  Goh Siong Thye. A new and fast implementation for null space based linear discriminant analysis. Pattern Recognition, 43, No.4 (2010):1373--1379.

[22] R. Huang and Delin Chu. Total nonpositivity of nonsingular matrices. Linear Algebra and Its Applications, 432, No.11 (2010):2931-2941.

[23] Delin Chu, Y.S. Hung and Hugo J. Woerdeman, Inertia and rank characterizations of some matrix expressions. SIAM Journal on Matrix Analysis and Applications, 31, No.3 (2009):1187--1226.

[24] Delin Chu, M.T. Chu and W.-W. Lin,  Quadratic model updating with symmetry, positive definiteness, and no spill-over. SIAM Journal on Matrix Analysis and Applications, 31, No.2 (2009):546--564.

[25] Delin Chu, M. Malabre and R. C. E. Tan,  State feedback decoupling problem with stability for $(A,B,C,D)$ quadruples. SIAM Journal on Matrix Analysis and Applications, 30, No.4 (2009):1735--1760.

[26] Delin Chu, Yuzo Ohta and D.D. Siljak, Inclusion principle for descriptor systems (Regular Paper). IEEE Transactions on Automatic Control, 54, No.1 (2009):3--18.

[27] Delin Chu and R. C. E. Tan. Algebraic characterizations for positive realness of descriptor systems. SIAM Journal on Matrix Analysis and Applications, 30, No.1 (2008):197--222.

[28] Delin Chu and R. C. E. Tan. The extended $J$-spectral factorization for descriptor systems (Regular Paper). Automatica, 44, No.3 (2008):585--597.

[29] Q.H. Chen, Delin Chu and R. C. E. Tan. Bilateral obstacle control problem of parabolic variational inequalities. SIAM Journal on Control and Optimization, 46, No.4 (2007):1518--1537.

[30] Z. J. Bai, Delin Chu and D. F. Sun, A dual optimization approach to inverse quadratic eigenvalue problems with partial eigenstructure. SIAM Journal on Scientific Computing}, 29, No.6 (2007):2531--2561.

[31] Z. J. Bai, Delin Chu and R. C. E. Tan, Computing the nearest doubly stochastic matrix with a prescribed entry. SIAM Journal on Scientific Computing, 29, No.2 (2007):635--655.

[32] Delin Chu, X. Liu and V. Mehrmann, A numerical method for computing the Hamiltonian Schur form. Numerische Mathematik, 105, No.3 (2007):375--412.

[33] Delin Chu, and Gene H. Golub, On a generalized eigenvalue problem for nonsquare pencils.

SIAM Journal on Matrix Analysis and Applications, 28, No.3 (2006):770--787.

[34] Delin Chu, and Y.S. Hung, A matrix pencil approach to the row by row decoupling problem for descriptor systems. SIAM Journal on Matrix Analysis and Applications, 28, No.3 (2006):682--702.

[35] Delin Chu, W.-W. Lin and R. C. E. Tan, A numerical method for a generalized algebraic Riccati equation. SIAM Journal on Control and Optimization, 45, No.4 (2006):1222--1250.

[36] Delin Chu and P. Van Dooren, A novel method for exact model matching problem with stability. Automatica, 42, No.10 (2006):1697--1704.

[37] Delin Chu and M. T. Chu, Low rank update of singular values. Mathematics of Computation, 75, No.255 (2006):1351--1366.

[38] Delin Chu and M. T. Chu, Reachable matrices by a QR step with shift. SIAM Journal on Applied Dynamical Systems, 5, No.1 (2006):91--107.

[39] Delin Chu and D. D. Siljak, A canonical form for the inclusion principle of dynamic systems. SIAM Journal on Control and Optimization, 44, No.3 (2005):969--990.

[40] Q.H. Chen, Delin Chu and R. C. E. Tan, Optimal control of obstacle for quasi-linear elliptic variational bilateral problems. SIAM Journal on Control and Optimization, 44, No.3 (2005):1067--1080.

[41] B. Y. Guo, Z. Q. Wang, Z. Su. Wan and Delin Chu, Second order Jacobi approximation with applications to fourth-order differential equations. Applied Numerical Mathematics, 55, No.4 (2005):480--502.

[42] Delin Chu and D. W. Ho, Computation of the $(J, J^\prime)$-lossless factorization for general rational matrices. SIAM Journal on Control and Optimization, 44, No.1 (2005):240--267.

[43] Delin Chu, On the numerical computation of the optimal $H_2$-norm and its associated fixed modes in $H_2$-optimization. Dynamics of Continuous, Discrete and Impulsive Systems, Series B: Applications $\&$ Algorithms, 12, No.1 (2005):111--128.

[44] Delin Chu and Y. S. Hung, A numerically reliable solution of squaring down problem in system design. Applied Numerical Mathematics, 51, No.2-3 (2004):221--241.

[45] Delin Chu,  On the computation of the infimum in $H_\infty$-optimization.  Numerical Linear Algebra with Applications, 11, No.7 (2004):619--648.

[46] Delin Chu, A constraint optimization problem in singular control theory: where is the nearest non-index-at-most-one matrix pencil? Dynamics of Continuous, Discrete and Impulsive Systems, Series B: Applications $\&$ Algorithms, 10, No.5 (2003):765--780.

[47] Delin Chu, The fixed-poles of disturbance decoupling problem and almost stability subspace $\cV_{b,g}^\star ({\rm Ker} C)$.  Numerische Mathematik, 96, No.2 (2003):221--252.

[48] Delin Chu, L. De Lathauwer and B. De Moor, A QR-type reduction for computing the SVD of a general matrix product/quotient.  Numerische Mathematik, 95, No.1 (2003):101--121.

[49] Delin Chu and M. Malabre, Numerically reliable design for proportional and derivative state feedback decoupling controller. Automatica, 38, No.12 (2002):2121--2125.

[50] Delin Chu and D. W. Ho, A new algorithm for an eigenvalue assignment problem from singular control theory. IEEE Transactions on Automatic Control, AC-47, No.7 (2002):1163--1167.

[51] Delin Chu, and M. Malabre, On the quadratic controllability and quadratic feedback minimality. IEEE Transactions on Automatic Control, AC-47, No.9 (2002):1487--1491.

[52] Delin Chu, and R. C. E. Tan, Solvability conditions and parameterization of all solutions for triangular decoupling problem. SIAM Journal on Matrix Analysis and Applications, 23, No.4 (2002):1171--1182.

[53] Delin Chu, and R. C. E. Tan, Numerically reliable computing for row by row decoupling problem with stability. SIAM Journal on Matrix Analysis and Applications, 23, No.4 (2002):1143--1170.

[54] Delin Chu, X. Liu and R. C. E. Tan, On the numerical computation of a structural decomposition for linear systems (Regular Paper). IEEE Transactions on Automatic Control, AC-47, No.11 (2002):1786--1799.

[55] Delin Chu, A case study of the open question: disturbance decoupling problem for singular systems by output feedback. IEEE Transactions on Automatic Control, AC-46, No.12 (2001):1924--1930.

[56] Delin Chu, and V. Mehrmann, Disturbance decoupling for linear time-invariant systems: a matrix pencil approach. IEEE Transactions on Automatic Control, AC-46, No.5 (2001):802--808.

[57] Delin Chu, L. De Lathauwer and B. De Moor, On the computation of restricted singluar value decomposition via cosine-sine decomposition. SIAM Journal on Matrix Analysis and Applications, 22, No.2 (2000):580--601.

[58] Delin Chu, Disturbance decoupled observer design for linear time-invariant systems: a matrix pencil approach. IEEE Transactions on Automatic Control, 45, No.8 (2000):1569--1575.

[59] Delin Chu, Matrix pencil characterizations of disturbance decoupling for linear time-invariant systems with direct feedthrough matrices. Internation Journal of Control, 73, No.11 (2000):1042--1050.

[60] Delin Chu, and V. Mehrmann, Disturbance decoupling for descriptor systems by state feedback. SIAM Journal on Control and Optimization, 38, No.6 (2000):1830--1858.

[61] Delin Chu, and Y. S. Hung, A numeriacl solution for simultaneous disturbance rejection and row by row decoupling problem. Linear Algebra and Its Applications, 320, No.1-3 (2000):37--49.

[62] Delin Chu, and V. Mehrmann, Disturbance decoupling for descriptor systems by measurement feedback. Electronic Journal on Linear Algebra, 7 (2000):152--173.

[63] Delin Chu, and B. De Moor, On the nonuniqueness of the factorization factors in the product singular value decomposition. Linear Algebra and Its Applications, 314, No.1-3 (2000):191--203.

[64] Delin Chu, and B. De Moor, On a variational formulation of QSVD and RSVD. Linear Algebra and Its Applications, 311, No.1-3 (2000):61--78.

[65] Delin Chu, and V Mehrmann, Disturbance decoupled observer design for descriptor systems. Systems $\&$ Control Letters, 38, No.1 (1999):37--48.

[66] Delin Chu, and D. W. Ho, Necessary and sufficient conditions for output feedback regularization of singular systems. IEEE Transactions on Automatic Control, AC-44, No.2 (1999):405--412.

[67] Delin Chu, and D. W. Ho, Infinite eigenvalue assignment for singular systems. Linear Algebra and Its Applications, 298, No.1-3 (1999):21--37.

[68] Delin Chu, V. Mehrmann and N. Nichols, Minimum norm regularization of descriptor systems by mixed output feedback. Linear Algebra and Its Applications, 296, No.1-3 (1999):39--77.

[69] Y. S. Hung and Delin Chu, $(J, J^\prime)$-lossless factorization for discrete-time systems. International Journal of Control, 71, No.3 (1998):517--533.

[70] Delin Chu, H. C. Chan and D. W. Ho, Regularization of singular systems by derivative and proportional output feedback. SIAM Journal on Matrix Analysis and Applications, 19, No.1 (1998):21--38.

[71] Y. S. Hung and Delin Chu, On extended $(J, J^\prime)$-lossless factorization. Linear Algebra and Its Applications, 271, No.1-3 (1998):117--138.

[72] Y. S. Hung and Delin Chu, Relationships between discrete-time and continuous-time algebraic Riccati inequalities. Linear Algebra and Its Applications, 270, No.1-3 (1998):287--313.

[73] Delin Chu, H. C. Chan and D. W. Ho, A general framework for state feedback pole assignment of singular systems. International Journal of Control, 67, No.2 (1997):135--152.

[74] W. H. Hui and Delin Chu, The optimal grid for steady Euler equations.  Computational Fluid Dynamics Journal, An International Journal, Japan, No.4 (1996):403--426.

[75] N. K. Nichols and Delin Chu, Regularization of descriptor systems. In Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory, (eds P. Benner, M. Bollhoefer, D. Kressner, C. Mehl and T. Stykel), Springer International Publishing, Switzerland, pp. 415--433, 2015.

[76] Delin Chu and Y.S. Hung, Numerical computation of the fixed poles in disturbance decoupling for descriptor systems, In Numerical Linear Algebra in Signals, Systems and Control

(eds P. Van Dooren, S. Bhattacharya, R. Chan, V. Olshevsky, A. Routray), 145--164. Germany:

Springer Verlag, 2011.