direct interpolation的意思|示意

'

English Words: Direct Interpolation

Direct interpolation is a mathematical method used to approximate values that lie between two known values. It is commonly used in mathematics and engineering to estimate a value of a function by inserting known values into an expression or equation.

Direct interpolation can be used to interpolate a variety of different types of functions. Most commonly, linear interpolation is used which assumes that the values follow a straight-line relationship between the two known points. This means that if two points, (x1, y1) and (x2, y2), are known, the value of a point lying between these two points can be estimated by the equation y=mx+c, where m is the slope and c is the y-intercept of the line that passes through these two points. The equation can be rearranged to find the value of the point that lies between the two known points as follows:

y= (y2-y1)/(x2-x1) x +y1 – (y2-y1)/(x2-x1)x1

Direct interpolation can also be used to interpolate more complex functions. For example, if two values of an exponential function, f(x) = ax^b, are known, then the value of the function lying between these two points, f(x) = ax^b, can be estimated by using the following formula:

f(x) = (f2-f1)/(x2-x1)*(x-x1) +f1

Direct interpolation is a useful mathematical technique for approximating values that lie between two known points. With the correct formula, it can be used to interpolate a variety of different types of functions, from linear to exponential. Furthermore, it can be used to estimate the value of a function without the need for a large amount of data.