id: 01200907
dt: j
an: 01200907
au: Chu, Moody T.; Guo, Quanlin
ti: A numerical method for the inverse stochastic spectrum problem.
so: SIAM J. Matrix Anal. Appl. 19, No.4, 1027-1039 (1998).
py: 1998
pu: Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
la: EN
cc: 
ut: nonnegative matrix; stochastic matrix; least squares; structured Markov
    chain; prescribed spectrum; steepest descent flow; isospectral
    matrices; singular value decomposition; numerical stability; numerical
    experiments
ci: 
li: doi:10.1137/S0895479896292418
ab: This paper concerns the construction of a stochastic matrix with a
    prescribed spectrum. The present “flow approach” is based on a
    differential equation to obtain the steepest descent flow for reducing
    the distance (given, say, in terms of the Frobenius norm) between
    isospectral matrices and nonnegative matrices. An analytic singular
    value decomposition helps to maintain the numerical stability of the
    flow and to monitor the promixity to singularity. The approach can be
    used for constructing Markov chains with specified properties. The
    paper includes results of numerical experiments performed on $5\times
    5$ matrices with MATLAB solvers.
rv: E.Kreyszig (Ottawa)