@article{chu_guo_1998, title={A numerical method for the inverse stochastic spectrum problem}, volume={19}, ISSN={["0895-4798"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0032339054&partnerID=MN8TOARS}, DOI={10.1137/S0895479896292418}, abstractNote={The inverse stochastic spectrum problem involves the construction of a stochastic matrix with a prescribed spectrum. The problem could be solved by first constructing a nonnegative matrix with the same prescribed spectrum. A differential equation aimed to bring forth the steepest descent flow in reducing the distance between isospectral matrices and nonnegative matrices, represented in terms of some general coordinates, is described. The flow is further characterized by an analytic singular value decomposition to maintain the numerical stability and to monitor the proximity to singularity. This flow approach can be used to design Markov chains with specified structure. Applications are demonstrated by numerical examples.}, number={4}, journal={SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS}, author={Chu, MT and Guo, QL}, year={1998}, month={Oct}, pages={1027–1039} }
 @article{chu_quanlin_1998, title={On the least squares approximation of symmetric-definite pencils subject to generalized spectral constraints}, volume={19}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0040581657&partnerID=MN8TOARS}, DOI={10.1137/s0895479895285135}, abstractNote={A general framework for the least squares approximation of symmetric-definite pencils subject to generalized eigenvalues constraints is developed in this paper. This approach can be adapted to different applications, including the inverse eigenvalue problem. The idea is based on the observation that a natural parameterization for the set of symmetric-definite pencils with the same generalized eigenvalues is readily available. In terms of these parameters, descent flows on the isospectral surface aimed at reducing the distance to matrices of the desired structure can be derived. These flows can be designed to carry certain other interesting properties and may be integrated numerically.}, number={1}, journal={SIAM Journal on Matrix Analysis and Applications}, author={Chu, Moody and Quanlin, G.}, year={1998}, pages={1–20} }