In the era of big data, we first need to manage the data, which requires us to find missing data or predict the trend, so we need operations including interpolation and data fitting. Interpolation is a process to discover deducing new data points in a range through known and discrete data points. When solving scientific and engineering problems, data points are usually obtained by sampling, experiments, and other methods. These data may represent a finite number of numerical functions in which the values of independent variables. According to these data, we often want to get a continuous function, i.e., curve; or more dense discrete equations are consistent with known data, while this process is called fitting. This article describes why the main idea come out logically and how to apply various method since the definitions are already written in the textbooks. At the same time, we give examples to help introduce the definitions or show the applications. We divide interpolation into several parts by their methods or functions for the structure. What comes first is the polynomial interpolation, which contains Lagrange interpolation and Newton interpolation, which are essential but critical. Then we introduce a typical stepwise linear interpolation - Neville's algorithm. If we are concerned about the derivative, it comes to Hermite interpolation; if we focus on smoothness, it comes to cubic splines and Chebyshev nodes. Finally, in the Data fitting part, we introduce the most typical one: the Linear squares method, which needs to be completed by normal equations.
翻译:在大数据时代,我们首先需要管理数据,这需要我们找到缺失的数据或预测趋势,因此我们需要包括内推和数据匹配在内的操作。 内插是一个通过已知和离散的数据点发现通过已知和离散的数据点在范围中显示新数据点的过程。 当解决科学和工程问题时, 数据点通常是通过抽样、 实验和其他方法获得的。 这些数据可能代表一个数量有限的数字函数, 其中独立变量的值。 根据这些数据, 我们常常想要获得一个连续的函数, 即曲线; 或更密集的离散方程式与已知的数据一致, 而这个过程被称作正常的。 此文章描述了为什么主要概念在逻辑上出现, 以及自定义已经在教科书中写入以来如何应用各种方法。 与此同时, 我们举例来帮助引入定义或显示应用程序。 我们用它们的方法或函数将内插的数个部分分隔。 根据这些数据, 我们通常想要获得一个连续的内插函数, 包含 Lagrange 内部和Newton 内插方程式, 它与已知的数据一致, 而这个过程又叫得恰妥。 然后, 我们引入一个典型的内定的内定式的内定式的内定式的内置法, 。