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Selected Articles (with L. Chen and L. Zhou) A linear homotopy method for computing generalized tensor eigenpairs, submitted (2015).Preprint.
(with L. Chen
and L. Zhou) Computing tensor eigenvalues via homotopy
methods, SIAM Journal on Matrix Analysis and Applications, 37(1), 2016,
pp.290-319. (http://dx.doi.org/10.1137/15M1010725) arXiv
preprint. (with J. Xu)
Proof of Stenger's conjecture on matrix $I^{(-1)}$ of Sinc methods,
Journal of Computational and Applied Mathematics, Vol. 255, 2014, pp.
805-811. (doi:
10.1016/j.cam.2013.07.001.) Preprint. (This paper has been awarded $300 monetary prize by Professor
Frank Stenger for proving his Sinc
matrix conjecture.) (with
D. Bunker and S. Zhang) A proximal ANLS algorithm for nonnegative tensor
factorization with a periodic enhanced line search, Applications of
Mathematics, 58(5), 2013, pp.493-509.( doi:10.1007/s10492-013-0026-2.) Preprint.
An unconstrained
optimization approach for finding real eigenvalues of even order symmetric
tensors, Numerical Algebra, Control, and Optimization, Vol. 3, No. 3, 2013,
pp.583-599.(doi:10.3934/naco.2013.3.583.) Preprint. (with
S. Friedland and S. Gaubert) Perron-Frobenius
theorem for nonnegative multilinear forms and extensions, Linear Algebra and
its Applications, Vol. 438, No. 2, 2013, pp.738-749.( doi:10.1016/j.laa.2011.02.042.) Preprint. (with
F. Gao and K. Schilling) On the rate of convergence of iterated exponentials,
Journal of Applied Mathematics and Computing, Vol. 39, 2012, pp.89-96.doi:
10.1007/s12190-011-0511-2
(with
F. Gao) Implementing the Nelder-Mead simplex
algorithm with adaptive parameters, Computational Optimization and
Applications, Vol. 51, No.1, 2012, pp. 259-277. doi: 10.1007/s10589-010-9329-3 ( Matlab code download: here ) (with
M. Neumann and U. Prasad) Alternating projected Barzilai-Borwein
methods for nonnegative matrix factorization, Electronic Transactions on
Numerical Analysis, Vol. 36, 2009-2010, pp. 54-82. ( Matlab code download: here ) (with
J. Han, M. Neumann, U. Prasad) On the convergence of the Image Space
Reconstruction Algorithm, Operators and Matrices, Vol. 3, No. 1, 2009, pp.
41-58. (with J. Axtell, D. Hershkowitz, M. Neumann, N. Sze) Optimization of the spectral radius of a product for nonnegative matrices, Linear Algebra and its Applications, Vol. 430, Issues 5-6, 2009, pp. 1442-1451. (with
M. Neumann) Inner product spaces, orthogonal projection, least squares, and
singular value decomposition, in Handbook of Linear Algebra, (editor: L.
Hogben), CRC Press, 2006. (with
M. Chen and M. Neumann) On single and double Soules
matrices, Linear Algebra and its Applications, Vol. 416, 2006, pp.88-110. (with
M. Neumann) Effect of dimensionality on the Nelder-Mead
simplex method, Optimization Methods and Software, Vol. 21, No. 1, 2006, pp.
1-16. (with
M. Catral, M. Neumann, and R. Plemmons) On reduced rank
nonnegative matrix factorization for symmetric nonnegative matrices, Linear
Algebra and its Applications, Vol. 393, 2004, pp.107-126. (with
G. Liu) On the convergence of the UOBYQA method, Journal of Applied
Mathematics and Computing, Vol. 16, No. 1-2, 2004, pp.125-142. (with
M. Neumann) Combining quasi-Newton and Cauchy directions, International
Journal of Applied Mathematics, Vol. 12, No.2, 2003, pp.167-191. (with
M. Neumann and J. Xu) On the roots of certain polynomials arising from the
analysis of the Nelder-Mead simplex method, Linear
Algebra and its Applications, Vol. 363, 2003, pp.109-124. (with
G. Liu and L. Jing) Convergence properties of the DFP algorithm for
unconstrained optimization, Optimization, Vol. 51, No. 2, 2002, pp.731-758. (with
G. Liu) A study of the Dennis-Wolkowicz method on
convex problems, Computational Optimization and Applications, Vol. 19, 2001,
pp.297-317. (with
G. Liu and L. Jing) A non-monotone Broyden method
for unconstrained optimization, Optimization Methods and Software, Vol. 15,
No. 2, 2001, pp.153-172. (with
M. Neumann and M. Tsatsomeros) Spectral radii of fixed Frobenius
norm perturbations of nonnegative matrices, SIAM Journal on Matrix Analysis
and Applications, Vol.21, No.1, 2000, pp.79-92. (with
G. Liu, L. Jing, and D. Han) A class of non-monotone conjugate gradient
methods for unconstrained optimization, Journal of Optimization Theory and
Applications, Vol.101, No.1, 1999, pp.127-140. (with
G. Liu) Global analysis of the Dennis-Wolkowicz
least-change secant algorithm, SIAM Journal on Optimization, Vol.8, No.3,
1998, pp.813-832. (with
L. Elsner, I. Koltracht,
M. Neumann, and M. Zippin) On a polygon equality
problem, Journal of Mathematical Analysis and Applications, Vol.223, 1998,
pp.67-75. (with
D. Han) Convergence analysis of the self-dual optimally conditioned SSVM
method of Oren-Spedicato, Optimization, Vol.37,
1996, pp.153-169. (with G. Liu) Global convergence of quasi-Newton methods for unconstrained optimization, Chinese Science Bulletin, No.7, 1996, pp.529-533. |
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