Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  deals with a method for the approximation of a spectral density function among the solutions of a generalized moment problem à la Byrnes/Georgiou/Lindquist. The approximation is pursued with respect to the Kullback-Leibler pseudo-distance, which gives rise to a convex optimization problem. After developing the variational analysis,  discuss the properties of an efficient algorithm for the solution of the corresponding dual problem, based on the iteration of a nonlinear map in a bounded subset of the dual space. Our main result is the proof of local convergence of the latter, established as a consequence of the central manifold theorem. Supported by numerical evidence,  conjecture that, in the mentioned bounded set, the convergence is actually global.
['Augusto Ferrante', 'Federico Ramponi', 'Francesco Ticozzi']
I am writing a research paper on a idea On the Convergence of an Efficient Algorithm for Kullback–Leibler Approximation of Spectral Densities
[{"from": "human", "value": "I am writing a research paper on a idea On the Convergence of an Efficient Algorithm for Kullback\u2013Leibler Approximation of Spectral Densities"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  deals with a method for the approximation of a spectral density function among the solutions of a generalized moment problem a\u0300 la Byrnes/Georgiou/Lindquist. The approximation is pursued with respect to the Kullback-Leibler pseudo-distance, which gives rise to a convex optimization problem. After developing the variational analysis,  discuss the properties of an efficient algorithm for the solution of the corresponding dual problem, based on the iteration of a nonlinear map in a bounded subset of the dual space. Our main result is the proof of local convergence of the latter, established as a consequence of the central manifold theorem. Supported by numerical evidence,  conjecture that, in the mentioned bounded set, the convergence is actually global."}]