Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider a recently published method for solving algebraic Riccati equations.  present a new perspective on this method in terms of the underlying linear-quadratic optimal control problem:  prove that the matrix obtained by this method expresses the optimal cost for a projected optimal control problem. The projection is determined by the so-called shift parameters of the method. Our representation in terms of the optimal control problem gives rise to a simple and very general convergence analysis.
['Arash Massoudi', 'Mark R. Opmeer', 'Timo Reis']
I am writing a research paper on a idea Analysis of an iteration method for the algebraic Riccati equation
[{"from": "human", "value": "I am writing a research paper on a idea Analysis of an iteration method for the algebraic Riccati equation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider a recently published method for solving algebraic Riccati equations.  present a new perspective on this method in terms of the underlying linear-quadratic optimal control problem:  prove that the matrix obtained by this method expresses the optimal cost for a projected optimal control problem. The projection is determined by the so-called shift parameters of the method. Our representation in terms of the optimal control problem gives rise to a simple and very general convergence analysis."}]