Sanzheng Qiao

Personal Information

Name:	Sanzheng Qiao
Position:	Professor Emeritus
Office Location:	ITB246
Telephone Number:	+1 (905)525-9140 ext. 27234
Electronic Address:	qiao@mcmaster.ca

Biography

Sanzheng Qiao was born in Shanghai, China in 1945. He received the B.S. degree from Shanghai Teachers' University, Shanghai, China in 1966, and the M.S. degree in computer science and Ph.D. degree in applied mathematics from Cornell University, Ithaca, NY, in 1986 and 1987 respectively.

He started at McMaster University, Hamilton, Ontario, Canada, in 1989 as an assistant professor. Now, he is a professor emeritus. His research interests include numerical linear algebra, distributed/parallel scientific computing, numerical methods for signal processing, and numerical software.

Course Information

COMP SCI 1MD3, Introduction to Programming
COMP SCI 2S03/SFWR ENG 2S03, Principles of Programming
COMP SCI 3MG3, Computer System Architecture
CAS 726, Parallel/Distributed Computing and Applications
CAS 727, Design of Numerical Software
CS/SE 3SH3, Operating Systems
SFWR ENG 3X03/COMP SCI 4X03, Scientific Computation
SFWR ENG 4F03 Design of Parallel/Distributed Computer Systems and Computations
CAS708/CSE700, Scientific Computation

Software

Erlang B Calculator.
Takagi factorization or symmetric SVD ( matlab )
Fast Square Hankel/Toeplitz SVD ( matlab )
Fast General Hankel/Toeplitz SVD ( matlab )
Block Lanczos tridiagonalization of complex symmetric matrices ( matlab, C )

Publications

Xuezhong Wang, Changxin Mo, Sanzheng Qiao, and Yimin Wei. Predefined-time convergent neural networks for solving the time-varying nonsingular multi-linear tensor equations. Neurocomputing. 2022, Vol. 472, 68--84.
pdf
Sanzheng Qiao, Yimin Wei, and Xuxin Zhang. Computing time-varying ML-weighted pseudoinverse by the Zhang neural networks. Numerical Functional Analysis and Optimization. 2020, Vol. 41, No. 14, 1672--1693, DOI: 10.1080/01630563.2020.1740887
pdf
Olatunji Oni and Sanzheng Qiao. Model-agnostic interpretation of cancer classification with multi-platform genomic data. BCB'19: Proceedings of the 10th ACM International Conference on Bioinformatics, Computational Biology and Health Informatics, Niagara Falls, NY USA, September, 2019, 34--41. DOI: 10.1145/3307339.3342189
pdf
Sanzheng Qiao and Yimin Wei. Acute perturbation of Drazin inverse and oblique projectors. Front. Math. China, Vol. 13, No. 6, 1427--1445, 2018.
pdf
Maolin Che, Sanzheng Qiao, and Yimin Wei. Adaptive algorithms for computing the principal Takagi vector of a complex symmetric matrix. Neurocomputing, Vol. 317, 79--87, 2018.
https://doi.org/10.1016/j.neucom.2018.07.064
pdf
Guorong Wang, Yimin Wei, and Sanzheng Qiao. Generalized Inverses: Theory and Computations, 2nd ed. Developments in Mathematics, Volume 53, Springer, 2018
ISSN 1389-2177, ISSN 2197-795X (electronic)
ISBN 978-981-13-0145-2, ISBN 978-981-13-0146-9 (eBook)
https://doi.org/10.1007/978-981-13-0146-9
Huai-An Diao, Liming Liang and Sanzheng Qiao. A condition analysis of the weighted linear least squares problem using dual norms. Linear and Multilinear Algebra. Vol. 66, No. 6, 1085-1103, 2018.
https://dx.doi.org/10.1080/03081087.2017.1337059
pdf
Sanzheng Qiao, Xue-Zhong Wang, and Yimin Wei. Two finite-time convergent Zhang neural network models for time-varying complex matrix Drazing inverse. Linear Algebra and its Applications. Vol. 542, 101-117, 2018.
https://dx.doi.org/10.1016/j.laa.2017.03.014
pdf
Huai-An Diao, Dongmei Liu and Sanzheng Qiao. Structured condition numbers and small sample condition estimation of symmetric Riccati equations. Applied Mathematics and Computation. Vol. 314, 2017, 80-97.
https://dx.doi.org/10.1016/j.amc.2017.06.028
pdf
Huai-An Diao, Yimin Wei, and Sanzheng Qiao. Structured condition numbers of structured Tikhonov regularization problem and their estimations. Journal of Computational and Applied Mathematics. Vol. 308, 2016, 276-300.
pdf
Huai-An Diao and Sanzheng Qiao. Structured condition numbers of symmetric algebraic Riccati equations. Proceedings of 2nd International Conference of Control, Dynamic Systems, and Robotics, Ottawa, Ontario, Canada, May 7-8, 2015.
pdf
Ling Lu, Wei Xu and Sanzheng Qiao. A fast SVD for multilevel block Hankel matrices with minimal memory storage. Numerical Algorithms. Vol. 69, No. 4, 2015, 875-891.
DOI: 10.1007/s11075-014-9930-0 (pdf)
Wen Zhang, Sanzheng Qiao and Yimin Wei. The diagonal reduction algorithm using fast Givens. Computer Mathematics. Editors: Ruyong Feng, Wen-shin Lee and Yosuke Sato. 453-465, 2014.
ISBN 978-3-662-43798-8 (Print) 978-3-662-43799-8 (Online) (pdf)
Filip Jeremic and Sanzheng Qiao. A Parallel Jacobi-type Lattice Basis Reduction Algorithm. International Journal of Numerical Analysis and Modeling, Series B. Vol. 5, No. 1-2, 2014, 1-12. (pdf)
Zhaofei Tian and Sanzheng Qiao. A Hybrid Method for Lattice Basis Reduction. Technical Report CAS-14-01-SQ, Department of Computing and Software, McMaster University, 1280 Main Street, Hamilton, Ontario, Canada L8S 4K1. (pdf)
Filip Jeremic and Sanzheng Qiao. A GPU Implementation of a Jacobi Method for Lattice Basis Reduction. Proceedings of International Workshop on Data-Intensive Scientific Discovery (DISD), 2013, Shanghai University, Shanghai, China, August 1-4, 2013. (pdf)
Zhaofei Tian and Sanzheng Qiao. An Enhanced Jacobi Method for Lattice-Reduction-Aided MIMO Detection. Proceedings of 2013 IEEE China Summit and International Conference on Signal and Information Processing (ChinaSIP), July 6-10, 2013, Beijing, China, 39-43.
DOI: 10.1109/ChinaSIP.2013.6625293 (pdf)
Huaian Diao, Weiguo Wang, Yimin Wei, and Sanzheng Qiao. On Condition Numbers for Moore-Penrose Inverse and Linear Least Squares Problem Involving Kronecker Products. Numerical Linear Algebra with Applications, 2013; 20:44-59.
DOI: 10.1002/nla.1823. (pdf)
Wen Zhang, Sanzheng Qiao, and Yimin Wei. HKZ and Minkowski Reduction Algorithms for Lattice-Reduction-Aided MIMO Detection. IEEE Transactions on Signal Processing. Vol. 60, No. 11, 2012, 5963-5976
DOI 10.1109/TSP.2012.2210708 (pdf)
Zhaofei Tian, Wen Zhang, Sanzheng Qiao. A Polynomial Time Jacobi Method for Lattice Basis Reduction. Technical Report CAS-12-04-SQ, Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada, L8S 4K1. (pdf)
Zhaofei Tian and Sanzheng Qiao. A Complexity Analysis of a Jacobi Method for Lattice Basis Reduction. Proceedings of C3S2E'12 the Fifth International C* Conference on Computer Science and Software Engineering. Editors: Bipin C. Desai, Sudhir Mudur, Emil Vassey. Montreal, Quebec, Canada, June 26-28, 2012. ACM International Conference Proceedings Series, ACM Press, New York, NY, 63-80. (pdf)
Sanzheng Qiao. A Jacobi Method for Lattice Basis Reduction. Proceedings of 2012 Spring World Congress on Engineering and Technology (SCET2012). Vol. 2. IEEE. May 27-30 2012, Xi'an, China. 649-652. (pdf)
Wen Zhang, Sanzheng Qiao, and Yimin Wei. A Diagonal Lattice Reduction Algorithm for MIMO Detection. IEEE Signal Processing Letters. Vol. 19, No. 5, 2012, 311-314.
DOI 10.1109/LSP.2012.2191614 (pdf)
Wen Zhang, Sanzheng Qiao, and Yimin Wei. Practical HKZ and Minkowski Lattice Reduction Algorithms. Department of Computing and Software, Technical Report CAS-11-04-SQ, McMaster University, Hamilton Ontario, Canada L8S 4K1. (pdf)
Yixian Luo and Sanzheng Qiao. A Parallel LLL Algorithm. Proceedings of the Forth International C* Conference on Computer Science and Software Engineering, 2011, Montreal, QC, Canada, May 16--18, 2011. ACM International Conference Proceedings Series, ACM Press, 93--101. (pdf)
Wen Zhang, Sanzheng Qiao, and Yimin Wei. Practical Algorithms for Constructing HKZ and Minkowski Reduced Bases. Department of Computing and Software, Technical Report CAS-11-03-SQ, McMaster University, Hamilton Ontario, Canada L8S 4K1. (pdf)
Wen Zhang, Yimin Wei, and Sanzheng Qiao. A Delayed Size-reduction Technique for Speeding Up the LLL Algorithm. Department of Computing and Software, Technical Report CAS-11-02-SQ, McMaster University, Hamilton Ontario, Canada L8S 4K1. (pdf)
Yixian Luo and Sanzheng Qiao. A Parallel LLL Algorithm. Department of Computing and Software, Technical Report CAS-10-03-SQ, McMaster University, Hamilton Ontario, Canada L8S 4K1. (pdf)
F.T. Luk, S. Qiao, and W. Zhang. A Lattice Basis Reduction Algorithm. Institute for Computational Mathematics Technical Report 10-04. Hong Kong Baptist University, Kowloon, Hong Kong, China. (pdf)
F.T. Luk and S. Qiao. A Pivoted LLL Algorithm. Linear Algebra Appl., 434(11), 2011, pp. 2296-2307.
Sanzheng Qiao. A Deterministic Method for Choosing Search Radii in Sphere Decoding. Proceedings of The 5th International Conference on Wireless Communications, Networking and Mobile Computing. Beijing, China, September 24-26, 2009.
http://ieeexplore.ieee.org/Xplore/guesthome.jsp
DOI: 10.1109/WICOM.2009.5304275
Weijia Yang and Sanzheng Qiao. A Novel Anonymization Algorithm: Privacy Protection and Knowledge Preservation. Expert Systems With Applications. 37(1), 2010, pp. 756-766. (pdf)
DOI: http://dx.doi.org/10.1016/j.eswa.2009.05.097
Franklin T. Luk and Sanzheng Qiao. Conditioning Properties of the LLL Algorithm, in Mathematics for Signal and Information Processing , edited by Schmalz, Ritter, Barrera, and Luk, Proc. of SPIE Vol. 7444 (2009), article 7444-17. (pdf)
Wei Xu and Sanzheng Qiao. A Twisted Factorization Method for Symmetric SVD of a Complex Symmetric Tridiagonal Matrix. Numerical Linear Algebra with Applications. 16(2009), 801-815. (pdf)
Liangmin Zhou, Yiqin Lin, Yimin Wei, Sanzheng Qiao. Perturbation Analysis and Condition Numbers of Symmetric Algebraic Riccati Equations. Automatica. 45(2009) 1005-1011. (pdf)
Don Morgan and Sanzheng Qiao. Analysis of Damped Mass-Spring Systems for Sound Synthesis. EURASIP Journal on Audio, Speech, and Music Processing. Vol. 2009, Article ID 947823, 19 pages, 2009. DOI: 10.1155/2009/947823.
http://www.hindawi.com/journals/asmp/2009/947823.html (pdf)
Liangmin Zhou, Lijing Lin, Yimin Wei, and Sanzheng Qiao. Perturbation Analysis and Condition Numbers of Scaled Total Least Squares Problems. Numerical Algorithms, 51, 2009, 381--399. (pdf)
DOI 10.1007/s11075-009-9269-0
Fei Zhao and Sanzheng Qiao. Radius Selection Algorithms for Sphere Decoding. Proceedings of C3S2E-09, ACM International Conference Proceedings Series. Edited by Bipin C. Desai and Carson K. Leung. Concordia University, Montreal, QC, May 19-21, 2009, pp. 169-174. (pdf)
Kevin Browne, Sanzheng Qiao, and Yimin Wei. A Lanczos Bidiagonalization Algorithm for Hankel Matrices. Linear Algebra and Its Applications, 430(2009), 1531-1543. (pdf)
Sanzheng Qiao, Wei Xu, and Yimin Wei. An Algorithm for Solving Scaled Total Least Squares Problems. The Proceedings of the 2008 International Conference on Scientific Computing, Worldcomp'08. Las Vegas, NE, July 14-17, 2008, pp.211-217. (pdf)
Don Morgan and Sanzheng Qiao. Accuracy and Stability in Mass-Spring Systems for Sound Synthesis. Proceedings of C3S2E-08, ACM International Conference Proceedings Series, edited by Bipin C. Desai. Concordia University, Montreal, QC, May 12-13, 2008, pp. 69-80. (pdf)
Sanzheng Qiao. Integer least squares: Sphere decoding and the LLL algorithm. Proceedings of C3S2E-08, ACM International Conference Proceedings Series, edited by Bipin C. Desai. Concordia University, Montreal, QC, May 12-13, 2008, pp. 23-28. (pdf)
Wei Xu and Sanzheng Qiao. A Divide-and-Conquer Method for the Takagi Factorization. SIAM J. Matrix Anal. Appl., 30/1(2008), 142-153. (pdf)
Wei Xu, Sanzheng Qiao, and Yimin Wei. A Note on the Scaled Total Least Squares Problem. Linear Algebra and Its Applications, 428/2+3(2008), 469-478. (pdf)
DOI link: http://dx.doi.org/10.1016/j.laa.2007.03.015.
Wei Xu and Sanzheng Qiao. A Fast SVD Algorithm for Square Hankel Matrices. Linear Algebra and Its Applications, 428/2+3(2008), 550-563. (pdf)
DOI link: http://dx.doi.org/10.1016/j.laa.2007.05.027
Franklin T. Luk and Sanzheng Qiao. Numerical Properties of the LLL Algorithm, in Advanced Signal Processing Algorithms, Architectures, and Implementations XVII, edited by Franklin T. Luk, Proc. of SPIE Vol. 6697-3, (2007). (pdf)
Yimin Wei, Huaian Diao, and Sanzheng Qiao. Condition Number for Weighted Least Squares Problem. Journal of Computational Mathematics, Vol.25, No.5, 2007, 561-572.
Wei Xu, Yimin Wei, and Sanzheng Qiao, Condition Numbers for Structured Least Squares, BIT, Vol. 46, No. 1, pp. 203--225, March 2006. (pdf)
Yimin Wei, Wei Xu, Sanzheng Qiao, and Huaian Diao. Componentwise Condition Numbers for Generalized Matrix Inversion and Linear Least Squares. Numerical Mathematics: A Journal of Chinese Universities, (English Series). 14(3), Aug. 2005, pp.277--286. (pdf)
Guohong Liu and Sanzheng Qiao, A High Performance C Package for Tridiagonalization of Complex Symmetric Matrices, Technical Report No. CAS 05-04-SQ, Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada. L8S 4K1. August 2005. (ps, pdf)
Wei Xu and Sanzheng Qiao, A Divide-and-Conquer Method for the Takagi Factorization, Technical Report No. CAS 05-01-SQ, Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada. L8S 4K1. February 2005. (ps, pdf)
Sanzheng Qiao, Guohong Liu, and Wei Xu. Block Lanczos Tridiagonalization of Complex Symmetric Matrices, in Advanced Signal Processing Algorithms, Architectures, and Implementations XV, edited by Franklin T. Luk, Proceedings of the SPIE Vol. 5910, 2005, pp. 285-295. (ps, pdf)
Wei Xu, Sanzheng Qiao, and Yimin Wei, An Algorithm for Solving Rank-Deficient Scaled Total Least Square Problems, Technical Report No. CAS 04-04-SQ, Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada. L8S 4K1. August 2004. (ps, pdf)
Sanzheng Qiao, Orthogonalization Techniques for the Lanczos Tridiagonalization of Complex Symmetric Matrices, Advanced Signal Processing Algorithms, Architectures, and Implementations XIV, edited by Franklin T. Luk, Proc. of SPIE Vol. 5559, 2004, pp. 423--434. (ps, pdf)
Yimin Wei, Huaian Diao, and Sanzheng Qiao, Condition Number for Weighted Linear Least Squares Problem and Its Condition Number, Technical Report No. CAS 04-02-SQ, Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada. L8S 4K1. May 2004. (ps, pdf)
Guorong Wang, Yimin Wei, and Sanzheng Qiao, Generalized Inverses: Theory and Computations, Graduate Series in Mathematics 5, Science Press, Beijing/New York, April 2004. ISBN 7-03-012437-5. Preface and Table of Contents (ps, pdf)
Huaian Diao, Yimin Wei, and Sanzheng Qiao, Displacement Rank of the Drazin Inverse, J. Comput. Appl. Math., 167(2004). 147--161. (pdf)
Guorong Wang and Sanzheng Qiao, Solving Constrained Matrix Equations and Cramer Rule, Applied Mathematics and Computation, 159/2 (2004) 333--340. (ps, pdf)
F.T. Luk and S. Qiao, A fast singular value algorithm for Hankel matrices, Fast Algorithms for Structured Matrices: Theory and Applications, Contemporary Mathematics 323, Editor V. Olshevsky, American Mathematical Society. 2003. 169--177. (ps, pdf)
Wei Xu, Yimin Wei, and Sanzheng Qiao, An Analysis of Rank-Deficient Scaled Total Least Squares Problem, Technical Report No. CAS 03-10-SQ, Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada. L8S 4K1. September 2003. (ps, pdf)
W.E. Larimore, F.T. Luk, and Sanzheng Qiao, Prediction Error Computation on a Grid, Proceedings of International Conference on Parallel Algorithms and Computing Environments, Editors Jun Zou and Xuebin. Chinese University of Hong Kong, Hong Kong, October 8--11, 2003, pp. 103--106. (ps, pdf)
Chengshu Guo and Sanzheng Qiao, A Stable Lanczos Tridiagonalization of Complex Symmetric Matrices, Technical Report No. CAS 03-08-SQ, Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada. L8S 4K1. July 2003. (Revised, September 2003.) (ps, pdf)
Yimin Wei and Sanzheng Qiao, The representation and approximation of the Drazin inverse of a linear operator in Hilbert space, Applied Mathematics and Computation, 138(2003) 77--89. (ps, pdf)
F.T. Luk, S. Qiao, and D. Vandervoorde, Exponential Decomposition and Hankel Matrix, Mathematics in Signal Processing V, Editors J.G. McWhirter and I.K. Proudler, Oxford University Press. June, 2002, 275-285. (pdf)
Sanzheng Qiao and Xiaohong Wang, Computing the Singular Vaues of 2-by-2 Complex Matrices, Software Quality Research Laboratory Report No. 5, Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada. L8S 4L7. June 2002. (ps, pdf). Revised December 2002
Xiaohong Wang and Sanzheng Qiao, A Parallel Jacobi Method for the Takagi Factorization, Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications, Vol. I, Editor H.R. Arabnia, pp. 206--212, Las Vegas, Nevada, USA, June, 2002.
S. Qiao and Jun Zhu, Exponential Decomposition Using Displacement Structure, Advanced Signal Processing Algorithms, Architectures, and Implementations XI, Franklin T. Luk, Editor, Proc. SPIE Vol. 4474, pp. 246--253, 2001.
F.T. Luk and S. Qiao, A Fast Singular Value Algorithm for Hankel Matrices, Advanced Signal Processing Algorithms, Architectures, and Implementations XI, Franklin T. Luk, Editor, Proc. SPIE Vol. 4474, pp. 254--261, 2001.
Yu Wu and Sanzheng Qiao, Parallel implementation of a validated method for initial value problems Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications, Vol. II, Editor: H.R. Arabnia, pp. 699--704, Las Vegas, Nevada, USA, June 25 - June 28, 2001.
S. Qiao and D.L. Parnas, Limitations of Backward Error Analysis SERG Report 389, Dept. of Computing and Software, McMaster University, Hamilton, Ontario, Canada, L8S 4L7, August, 2000.
Dan Yan, Polina Galkin, and Sanzheng Qiao, Global Meeting Plus (GMP) Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications, Vol. III, Editor: H.R. Arabnia, pp. 1689--1695, Las Vegas, Nevada, USA, June 26 - June 29, 2000.
S. Qiao and S. Wang, Automatically Testing Numerical Stability SERG Report 385, Dept. of Computing and Software, McMaster University, Hamilton, Ontario, Canada, L8S 4L7, May 2000.
W. Gao and S. Qiao, Multithreaded Implementation of a Biomolecular Sequence Alignment Algorithm, Proceedings of Canadian Conference on Electrical and Computer Engineering, May 7--10, 2000, Halifax, Nova Scotia, Canada.
Adam Bojanczyk, Sanzheng Qiao, and Allan O. Steinhardt, Unifying Unitary and Hyperbolic Transformations, Linear Algebra and Its Applications, 316(2000), pp.183--197.
F.T. Luk and S. Qiao, A Fast Eigenvalue Algorithm for Hankel Matrices, Linear Algebra and Its Applications, 316(2000), pp.171--182. (ps, pdf)
F.T. Luk and S. Qiao, Analysis of a Fast Hankel Eigenvalue Algorithm, in Advanced Signal Processing Algorithms, Architectures, and Implementations IX, Franklin T. Luk, Editor, Proc. SPIE Vol. 3807, pp. 324-333, 1999. (ps, pdf)
S. Qiao and H. Zhang, An Automatic Logfile Analyzer for Parallel Programs, Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications, Vol. III, Editor: H.R. Arabnia, pp. 1371-1376, Las Vegas, Nevada, USA, June 28 - July 1, 1999. ( compressed ps, revised)
W. Xiong, J. Li, R.M.M. Chen, and S. Qiao, A Fast Decomposition of Banded Symmetric Toeplitz Matrices for Parallel Processing, Proceedings of IEEE International Symposium on Circuits and Systems, Vol. III, pp. 259-262, Orlando, Florida, May 30 - June 2, 1999.
S. Qiao, Analysis of a Fast Eigenvalue Algorithm for Hankel Matrices, Technical Report CAS99-05, Department of Computing and Software, McMaster University, Ontario, Canada, L8S 4L7, June 1999.
S. Qiao, Analysis of the Unified Transformations, Technical Report CAS99-03, Department of Computing and Software, McMaster University, Ontario, Canada, L8S 4L7, March 1999.
K. Kreyman, D.L. Parnas, and S. Qiao, Inspection Procedures for Critical Programs that Model Physical Phenomena, Technical Report No. 368, Communications Research Laboratory, McMaster University, Ontario, Canada, L8S 4K1, February 1999. ( pdf)
S. Qiao and L. Qiao. A Robust and Efficient Algorithm for Evaluating Erlang B Formula. Technical Report CAS98-03, Department of Computing and Software, McMaster University, Ontario, Canada, L8S 4L7, August 1998. (ps, pdf)
An Erlang B Calculator, (new) is available.
F.T. Luk and S. Qiao, A Fast Eigenvalue Algorithm for Hankel Matrices, Advanced Signal Processing: Algorithms, Architectures, and Implementations VIII, Franklin T. Luk, Editor, Proc. SPIE Vol. 3461, pp.249--256, July 1998.
S. Qiao and W.S-Y. Wang, Evaluating Phylogenetic Trees by Matrix Decomposition, Anthropological Science, 106(1), 1-22, 1998.
S. Qiao, Unifying Unitary and Hyperbolic Rotations and Reflectors, Technical Report No. 98-05, Department of Computer Science and Systems, McMaster University, Ontario, Canada, January 1998.
S. Qiao and W. S-Y Wang, A Matrix Representation of Phylogenetic Trees, The Proceedings of the Third Annual International Computing and Combinatorics Conference (COCOON'97), Editors: Tao Jiang and T.D. Lee, Lecture Notes in Computer Science 1276, Springer, pp.274--283, Shanghai, China, August, 1997.
F.T. Luk and S. Qiao, Using Complex-Orthogonal Transformations to Diagonalize a Complex Symmetric Matrix, Advanced Signal Processing: Algorithms, Architectures, and Implementations VII, Franklin T. Luk, Editor, Proc. SPIE Vol. 3162, pp.418--425, July 1997.
S. Qiao and Sheldon Siu-tung Tam, Parallel Implementation of a Matrix Decomposition Method for Evaluatiing Phylogenetic Trees, The Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA'97), Volume II, Editor: H.R. Arabnia, pp.774--777, Las Vegas, NV, June, 1997.
S. Qiao, R.M.M. Chen, and X.D. Jia, A QR Decomposition Based Algorithm for Computing Transfer Functions From State Equation, 1997 IEEE International Symposium on Circuits and Systems, Hong Kong, June, 1997.
M.K. Ng, R.J. Plemmons, and S. Qiao, Regularized Blind Deconvolution using Recursive Inverse Filtering, Workshop on Scientific Computing, Hong Kong, March, 1997. (invited lecture)
A revision appeared in IEEE Trans. Image Processing, Vol. 9, No. 6, 2000. pp. 1130--1134.
Click here for more on aero-optics research.
F.T. Luk and S. Qiao, Decaying Exponentials and Signal Decomposition, Mathematics in Signal Processing, Edited by J.G. McWhirter and I.K. Proudler, Oxford University Press, 1998, pp. 175-186. ISBN 0-19-850202-8. (Based on the proceedings of a conference on Mathematics in Signal Processing. Organized by the Institute of Mathematics and its Applications and held at the University of Warwick, UK, 17-19 December 1996.)
F.T. Luk and S. Qiao, A Symmetric Rank-Revealing Toeplitz Matrix Decomposition, Journal of VLSI Signal Processing, Vol. 14, No. 1, pp.19--28, Oct. 1996.
F.T. Luk and S. Qiao, An Adaptive Algorithm for Interference Cancelling in Array Processing, Advanced Signal Processing Algorithms, Architectures, and Implementations VI, Franklin T. Luk, Editor, SPIE Proceedings Vol. 2846, 151--161(1996).
F.T. Luk and S. Qiao, Rank-Revealing Decomposition of Symmetric Toeplitz Matrices, Advanced Signal Processing Algorithms , Franklin T. Luk, Editor, SPIE Proceedings Vol. 2563, 293--301(1995).
S. Qiao, Approximating the PSVD and QSVD, SVD and Signal Processing, III: Algorithms, Architectures and Applications, edited by Marc Moonen and Bart De Moor, Elsevier, pp. 149-155, 1995.
Sanzheng Qiao