Lecture 7: Intro to Geometry, Splines, and Bezier Curves (21)
ML2000-LT
In mathematics, a spline is a special function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher degrees. Therefore a higher order polynomial does not necessarily yield better results than the 3rd order, due to Runge's phenomenum, and Runge's phenomenum is is a problem of oscillation at the edges of an interval that occurs when using polynomial interpolation with polynomials of high degree over a set of equispaced interpolation points.
In mathematics, a spline is a special function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher degrees. Therefore a higher order polynomial does not necessarily yield better results than the 3rd order, due to Runge's phenomenum, and Runge's phenomenum is is a problem of oscillation at the edges of an interval that occurs when using polynomial interpolation with polynomials of high degree over a set of equispaced interpolation points.