What Is Linear Interpolation?
Estimating values between two known points can be done using a technique called linear interpolation, which is also referred to as "playing connect the dots." Imagine you are trying to predict the temperature at three o'clock in the afternoon, given the information that it was eighty degrees at two o'clock and eighty-five degrees at four o'clock. The fundamental premise upon which linear interpolation is constructed is that if a straight line connects two points, then any point on that line can be characterized by a straightforward linear equation. This idea forms the basis of linear interpolation. Therefore, if we have two known points (x1, y1) and (x2, y2), we can use the slope of the line that connects those two points to estimate the value of y for any other value of x between x1 and x2. This is possible because the slope of the line is proportional to the distance between the two points. There are many different applications for linear interpolation, such as in the field of computer graphics, where it can be used to round off the edges of digital images, or in the field of meteorology, where it can be used to estimate the temperature at a particular time and location based on data collected from weather stations. It is also used in finance and economics, where it can be used to estimate future values of stock prices or currency exchange rates based on historical data. Both of these fields make use of financial modeling. In these areas, it is also frequently combined with other methods of interpolation, such as polynomial or spline interpolation, to improve the accuracy of the results. To estimate values between two known points, one can use linear interpolation, which is both straightforward and time-effective. It is predicated on the notion that if a straight line connects two points, then any point on that line can be described by a straightforward linear equation and that this notion underpins the concept. It finds application in many different areas, including computer graphics, meteorology, finance, and economics, to name a few. #InterpolationMethods
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