插值和外插的区别

1. 插值：
插值是指从一个值序列中给出的两个已知值估计单个值。

2. 外推：
外推是指从给定的值序列中估计单个值，其中值的背景在特定时间是已知的。

更准确地说，我们可以定义插值和外插如下：

假设我们给出了函数f(x) 的以下列表值，这些值对应于 x 的一组离散值：

插值是查找与x ₀和 x _n之间的任何未列出的 x 值相对应的 f(x) 值的过程。为给定范围 [x0, xn] 之外的某个 x 值找到 f(x) 值的过程称为外推。它假设 f(x) 在给定范围之外的行为与 f(x) 在给定范围内的行为相同，这可能并不总是有效的。

插值和外插的区别如下：

Sr. No.	Interpolation	Extrapolation
1.	Interpolation means reading a value which lies between two extreme points.	Extrapolation means reading a value which lies outside two extreme values.
2.	It supplies us the missing link.	It helps in forecasting.
3.	It refers to the insertion of an intermediate value in the series of terms.	It refers to projecting a value for the future.
4.	It can be calculated graphically. It is one of the simplest method of interpolation.	Graphic method is not applied for extrapolation.
5.	When records of some period are lost, figures relating to such projects may be estimated to complete the records by interpolation.	It plays significant role in economic planning. For economic planning, projection of future data is essential. This is done by extrapolation.
6.	It is the estimation of a most likely estimate in given conditions. The technique of estimating a past figure in termed as interpolation.	Estimating a probable figure for future is called extrapolation.
7.	Interpolation is preferred because we have a greater likelihood of obtaining a valid estimate.	In extrapolation, we are making the assumption that our observed trend continues for values of x outside the range. We used to form our model. This may not be the case. So we must be very careful while using extrapolation.