Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A quite comprehensive theory of analytic interpolation with degree constraint, dealing with rational interpolants with an a priori bound, has been developed in recent years.   consider the limit case when this bound is removed, and only stable interpolants with a prescribed maximum degree are sought. This leads to ighted  H   2  minimization, where the interpolants are parameterized by the ights. The inverse problem of determining the ight and the interpolation points given a desired interpolant profile is considered, and a rational approximation procedure based on the theory is proposed. This provides a tool for tuning the solution to specifications. The basic idea could also be applied to the case with bounded interpolants.
['Johan Karlsson', 'Anders Lindquist']
I am writing a research paper on a idea Stable rational approximation in the context of interpolation and convex optimization
[{"from": "human", "value": "I am writing a research paper on a idea Stable rational approximation in the context of interpolation and convex optimization"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A quite comprehensive theory of analytic interpolation with degree constraint, dealing with rational interpolants with an a priori bound, has been developed in recent years.   consider the limit case when this bound is removed, and only stable interpolants with a prescribed maximum degree are sought. This leads to ighted  H   2  minimization, where the interpolants are parameterized by the ights. The inverse problem of determining the ight and the interpolation points given a desired interpolant profile is considered, and a rational approximation procedure based on the theory is proposed. This provides a tool for tuning the solution to specifications. The basic idea could also be applied to the case with bounded interpolants."}]