M-spline

In the mathematical subfield of numerical analysis, an M-spline[1][2] is a non-negative spline function.

A family of M-spline functions of order k with n free parameters is defined by a set of knots t1  ≤ t2  ≤  ...  ≤  tn+k such that The family includes n members indexed by i = 1,...,n. An M-spline Mi(x|k, t) has the following mathematical properties M-splines can be efficiently and stably computed using the following recursions: For k = 1, if ti ≤ x < ti+1, and Mi(x|1,t) = 0 otherwise.

For k > 1, M-splines can be integrated to produce a family of monotone splines called I-splines.

M-splines can also be used directly as basis splines for regression analysis involving positive response data (constraining the regression coefficients to be non-negative).

This applied mathematics–related article is a stub.

An M-spline family of order three with four interior knots.