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).
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