What is the difference between interpolation and approximation

Active 2 years, 8 months ago. Viewed 2k times. Tanner 1. James James 3, 3 3 gold badges 11 11 silver badges 43 43 bronze badges. Add a comment.

Active Oldest Votes. Gare G. Gare 1, 6 6 silver badges 20 20 bronze badges. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Upcoming Events. You might have heard term linear regression. It is a special case of polynomial approximation: an approximation of some data with a line, plane or hyperplane.

So now you know how that works too. There are three more facts I want to share, but I think it would be more fun if you reveal them yourself with a living plot from above. Every time you find something interesting, a new fact will appear below. Fact 1. When the number of points equals the degree of polynomial plus one, the approximation fits all the points perfectly.

Another words, approximation becomes interpolation. Fact 2. When polynomial degree is 0, the function is technically not a polynomial anymore, but a constant. Still, approximation method works even for a constant.

Fact 3. When you put several points in one place, that place attracts polynomial more than other points. This makes sense, since the polynomial minimizes the squared residuals sum. If some point occurs more than once, then it influences the sum more.

That's how you do weighted approximation. You can add weights to your points by multiplying them. When you have a set of points, you use interpolation to find values between these points. With polynomial interpolation , it is about finding a polynomial that runs exactly through the points we want. You can add and remove points, but you can't select a polynomial degree now since it depends on the number of points. Just write this down for every point, put it into the matrix form and here you go.

Painting and drawing tools in multimedia, Painting and Drawing Tools Pa Applications of ray tracing - modeling and rendering , Applications of Ray Opengl, difference between gl,glu and glut difference between gl,glu and glut.

Introduction of viewing transformations, Introduction of Viewing Transfor Use the midpoint circle algorithm to get the output, Figure uses three dash Write Your Message! Email id. Verfication Code. Featured Services. Online Tutoring. Project Development. Exam Preparation. Course Help. Assignment Help. Popular Subjects. HR Management. Computer Science. Web Design. Submit Assignment. All rights reserved! Interpolation of surface - polygon rendering, Interpolation of surface - Po