论文标题
构建分段的可区分四边形以确定算法运行时间并建模非物质功能
Constructing Segmented Differentiable Quadratics to Determine Algorithmic Run Times and Model Non-Polynomial Functions
论文作者
论文摘要
我们提出了一种方法来确定算法效率的持续进展，作为时间复杂性的标准计算的替代方法，可能但不仅仅是仅在处理具有未知最大索引的数据结构时，并且算法取决于与输入大小相距于多个变量的算法。提出的方法可以有效地确定任何给定索引$ x $的运行时间行为$ f $，以及仅通过组合$ \ frac {n} {2} {2} $ Quadratic sev，根据一个或多个参数的函数，是一个或多个参数的函数，是一个或多个参数的函数。 Although the approach used is designed for analyzing the efficacy of computational algorithms, the proposed method can be used within the pure mathematical field as a novel way to construct non-polynomial functions, such as $\log_2{n}$ or $\frac{n+1}{n-2}$, as a series of segmented differentiable quadratics to model functional behavior and reoccurring natural patterns.测试后，我们的方法的平均准确度高于99 \％，在功能相似性方面。
We propose an approach to determine the continual progression of algorithmic efficiency, as an alternative to standard calculations of time complexity, likely, but not exclusively, when dealing with data structures with unknown maximum indexes and with algorithms that are dependent on multiple variables apart from just input size. The proposed method can effectively determine the run time behavior $F$ at any given index $x$ , as well as $\frac{\partial F}{\partial x}$, as a function of only one or multiple arguments, by combining $\frac{n}{2}$ quadratic segments, based upon the principles of Lagrangian Polynomials and their respective secant lines. Although the approach used is designed for analyzing the efficacy of computational algorithms, the proposed method can be used within the pure mathematical field as a novel way to construct non-polynomial functions, such as $\log_2{n}$ or $\frac{n+1}{n-2}$, as a series of segmented differentiable quadratics to model functional behavior and reoccurring natural patterns. After testing, our method had an average accuracy of above of 99\% with regard to functional resemblance.
