弱化缓冲算子作用强度及光滑性比较

针对弱化缓冲算子作用强度和光滑性问题, 提出缓冲率的概念, 比较了加权调和平均算子、加权几何平均算子、加权算术平均算子、加权平方平均算子、及其多阶算子的作用强度大小; 分析了弱化缓冲算子作用强度与光滑性之间的关系, 并加以实例验证. 结果表明, 对于单调递增序列, 加权调和平均算子、加权几何平均算子、加权算术平均算子、加权平方平均算子的作用强度依次增强, 单调递减时依次减弱; 多阶弱化缓冲算子的作用强度随阶数的递增而增强; 弱化缓冲算子的作用强度与光滑性具有内在一致性, 这为弱化缓冲算子光滑性的大小比较提供了新途径.

Comparison of operator strength and smoothness between common weakening buffer and their multi-order operators

On account of the problem for operator strength and smoothness of weakening buffer operator, the concept of buffer ratio is introduced. We compare operator strength among different common weakening buffer operators and their multi-order buffer operators, and analyze the relationship between operator strength and smoothness of the weakening buffer operator. Both of which are varied by examples. The results show that, for monotonically increasing sequence, the operator strength of the weighted harmonic mean operator, the weighted geometric mean operator, the weighted arithmetic mean operator, the weighted quadratic mean operator are boosting up, and the operator strength of four operators are contrary for monotonically decreasing sequence. Whether the sequence is increasing or decreasing monotonically, the operator strength of multi-order weakening buffer operator is increasing with the order increased. There is internal consistency between operator strength and smoothness, which provide a new way to compare smoothness of weakening buffer operator.