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In mathematics, a spline is a 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.
In the mathematical field of numerical analysis, spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a spline. That is, instead of fitting a single, high-degree polynomial to all of the values at once, spline interpolation fits low-degree polynomials to small subsets of the ...
In the mathematical subfield of numerical analysis, a B-spline or basis spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition. Any spline function of given degree can be expressed as a linear combination of B-splines of that degree. Cardinal B-splines have knots that are ...
The interpolated surface (meaning the kernel shape, not the image) is smoother than corresponding surfaces obtained by bilinear interpolation or nearest-neighbor interpolation. Bicubic interpolation can be accomplished using either Lagrange polynomials, cubic splines, or cubic convolution algorithm.
See also Subdivision surfaces, which is an emerging alternative to spline-based surfaces. Pages in category "Splines (mathematics)" The following 30 pages are in this category, out of 30 total.
A box spline is a multivariate function defined for a set of vectors, , usually gathered in a matrix := […]. When the number of vectors is the same as the dimension of the domain (i.e., N = d {\displaystyle N=d} ) then the box spline is simply the (normalized) indicator function of the parallelepiped formed by the vectors in Ξ {\displaystyle ...
The most familiar example is the cubic smoothing spline, ... The thin plate splines are isotropic, meaning that if we rotate the , co-ordinate system the estimate ...
In the mathematical subfield of numerical analysis, an M-spline [1] [2] is a non-negative spline function. An M-spline family of order three with four interior knots. Definition