spline
spline In its simplest form a spline function (of degree n), s(x), is a piecewise polynomial on [x1,xN] that is (n – 1) times continuously differentiable, i.e. s(x) ≡ polynomial of degree n xi←x←xi+1, i = 1,2,…,N–1
These polynomial “pieces” are all matched up at points (called knots): x1 < x2 < … < xN
in the interior of the range, so that the resulting function s(x) is smooth. The idea can be extended to functions of more than one variable. Cubic splines – spline curves of degree 3 – provide a useful means of approximating data to moderate accuracy. Splines are often the underlying approximations used in variational methods. See also B-spline.
These polynomial “pieces” are all matched up at points (called knots): x1 < x2 < … < xN
in the interior of the range, so that the resulting function s(x) is smooth. The idea can be extended to functions of more than one variable. Cubic splines – spline curves of degree 3 – provide a useful means of approximating data to moderate accuracy. Splines are often the underlying approximations used in variational methods. See also B-spline.
More From encyclopedia.com
NEARBY TERMS
spline