径向基函数?
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径向基函数?
径向基函数?
径向基函数?
基于径向基函数强形式的无单元（RBFS）法是真正意义上的无单元方法,但为了追求精度要求却未达到稀疏化.本文对RBFS进行了改进,通过构造具有占函数性质的形函数,得到了具有稀疏带状性的系数矩阵,提高了计算效率,同时具有RBFS方法的优点.通过求解微分方程,得到节点均布时影响域半径与求解精度的关系曲线,验证了基函数中自由参数最佳取值的计算公式的适用性；并把节点均布下得到的影响域半径和自由参数的规律应用到节点任意排列的情况下,求解结果变化不大,均满足精度要求,由此得出这些规律仍然适用,这种无单元法对节点位置不敏感.
A radial basis function (RBF) is a real-valued function whose value depends only on the distance from the origin, so that ; or alternatively on the distance from some other point c, called a center, s...
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A radial basis function (RBF) is a real-valued function whose value depends only on the distance from the origin, so that ; or alternatively on the distance from some other point c, called a center, so that . Any function that satisfies the property is a radial function. The norm is usually Euclidean distance, although other distance functions are also possible. For example by using Lukaszyk-Karmowski metric, it is possible for some radial functions to avoid problems with ill conditioning of the matrix solved to determine coefficients wi (see below), since the is always greater than zero.[1]
Sums of radial basis functions are typically used to approximate given functions. This approximation process can also be interpreted as a simple kind of neural network.
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