What are the differences between curve fitting and interpolation?

Interpolation is to connect discrete data points so that one can get reasonable estimates of data points between the given points. Curve fitting is to find a curve that could best indicate the trend of a given set of data.

What is interpolation in curve fitting?

Interpolation is a method of estimating values between known data points. Use interpolation to smooth observed data, fill in missing data, and make predictions. Curve Fitting Toolbox™ functions allow you to perform interpolation by fitting a curve or surface to the data.

Can interpolation and curve fitting be used interchangeably?

You can use many different methods for interpolation including linear interpolation and polynomial, or spline curves. When you are fitting curve to the data it is up to you to decide how close do you want it to fit the data. Nothing stops you from choosing the curve that perfectly fits to your data.

What are the methods used in interpolation and curve fitting?

This chapter covers three types of techniques, i.e. the Newton interpolation, the Lagrange interpolation and the Spline interpolation. The resulting equation can be used for curve fitting.

What’s the difference between regression and interpolation?

Regression is the process of finding the line of best fit[1]. Interpolation is the process of using the line of best fit to estimate the value of one variable from the value of another, provided that the value you are using is within the range of your data.

What is the difference between linear interpolation and polynomial interpolation?

Polynomial interpolation is a generalization of linear interpolation. Note that the linear interpolant is a linear function. The interpolation error is proportional to the distance between the data points to the power n. Furthermore, the interpolant is a polynomial and thus infinitely differentiable.

What is the difference between interpolation and extrapolation give suitable examples?

When we predict values that fall within the range of data points taken it is called interpolation. When we predict values for points outside the range of data taken it is called extrapolation. The same process is used for extrapolation. A sample with a mass of 5.5 g, will have a volume of 10.8 ml.

What is the difference between linear curve fitting and interpolation?

In interpolation, the targeted function should pass through all given data points whereas in linear curve fitting we find the general trend of dependent variable. The cost function could be the distance between them. If we keep on going with same sense of cost function, are not in case of interpolation the difference between data points zero?

What are the different methods of interpolation?

You can use many different methods for interpolation including linear interpolation and polynomial, or spline curves. When you are fitting curve to the data it is up to you to decide how close do you want it to fit the data. Nothing stops you from choosing the curve that perfectly fits to your data.

What is the source of the data in a curve fitting?

The source of the data may be experimental observations or numerical computations. There is a distinction between interpolation and curve fitting. In interpolation we construct a curve through the data points. In doing so, we make the implicit assumption that the data points are accurate and distinct.

What is curcurve fitting?

Curve fitting is applied to data that contain scatter (noise), usually due to measurement errors. Here we want to find a smooth curve that approximates the data in some sense. Thus the curve does not necessarily hit the data points. The difference between interpolation and curve fitting is illustrated in Fig. 3.1.