Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  develops some mollification formulas involving convolutions beten popular radial basis function (RBF) basic functions Φ, and suitable mollifiers. Polyharmonic splines, scaled Bessel kernels (Matern functions) and compactly supported basic functions are considered. A typical result is that in ℛd the convolution of |{•}|β and (•2+c2)−(β+2d)/2 is the generalized multiquadric (•2+c2)β/2 up to a multiplicative constant. The constant depends on c>0, β, where ℜ(β)>−d, and d. An application which motivated the development of the formulas is a technique called implicit smoothing. This computationally efficient technique smooths a previously obtained RBF fit by replacing the basic function Φ with a smoother version Ψ during evaluation.
['R. K. Beatson', 'H.-Q. Bui']
I am writing a research paper on a idea Mollification formulas and implicit smoothing.
[{"from": "human", "value": "I am writing a research paper on a idea Mollification formulas and implicit smoothing."}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  develops some mollification formulas involving convolutions beten popular radial basis function (RBF) basic functions \u03a6, and suitable mollifiers. Polyharmonic splines, scaled Bessel kernels (Matern functions) and compactly supported basic functions are considered. A typical result is that in \u211bd the convolution of |{\u2022}|\u03b2 and (\u20222+c2)\u2212(\u03b2+2d)/2 is the generalized multiquadric (\u20222+c2)\u03b2/2 up to a multiplicative constant. The constant depends on c>0, \u03b2, where \u211c(\u03b2)>\u2212d, and d. An application which motivated the development of the formulas is a technique called implicit smoothing. This computationally efficient technique smooths a previously obtained RBF fit by replacing the basic function \u03a6 with a smoother version \u03a8 during evaluation."}]