Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   discuss the problem of approximation of the first derivative of a function at the endpoint of its definition interval. This problem is motivated by diabetes therapy management, where it is important to provide estimations of the future blood glucose trend from current and past measurements. A natural way to approach the problem is to use one-sided finite difference schemes for numerical differentiation, but, following this way, one should be aware that the values of the function to be differentiated are noisy and available only at given fixed points. Then (as  argue in the paper) the number of used point values is the only parameter to be employed for regularization of the above mentioned ill-posed problem of numerical differentiation.   present and theoretically justify an adaptive procedure for choosing such a parameter.  also demonstrate some illustrative tests, as ll as the results of numerical experiments with simulated clinical data.
['Valeriya Naumova', 'Sergei V. Pereverzyev', 'Sivananthan Sivananthan']
I am writing a research paper on a idea Adaptive parameter choice for one-sided finite difference schemes and its application in diabetes technology
[{"from": "human", "value": "I am writing a research paper on a idea Adaptive parameter choice for one-sided finite difference schemes and its application in diabetes technology"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   discuss the problem of approximation of the first derivative of a function at the endpoint of its definition interval. This problem is motivated by diabetes therapy management, where it is important to provide estimations of the future blood glucose trend from current and past measurements. A natural way to approach the problem is to use one-sided finite difference schemes for numerical differentiation, but, following this way, one should be aware that the values of the function to be differentiated are noisy and available only at given fixed points. Then (as  argue in the paper) the number of used point values is the only parameter to be employed for regularization of the above mentioned ill-posed problem of numerical differentiation.   present and theoretically justify an adaptive procedure for choosing such a parameter.  also demonstrate some illustrative tests, as ll as the results of numerical experiments with simulated clinical data."}]