Definition
A spline is a piecewise-polynomial real function
on an interval composed of k ordered disjoint subintervals with
- .
The restriction of S to an interval i is a polynomial
- ,
so that
The highest order of the polynomials is said to be the order of the spline S. If all subintervals are of the same length, the spline is said to be uniform and non-uniform otherwise.
The idea is to choose the polynomials in a way that guarantees sufficient smoothness of S. Specifically, for a spline of order n, S is required to be continuously differentiable to order n-1 at the interior points : for all and all ,
.
Read more about this topic: Spline (mathematics)
Famous quotes containing the word definition:
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)
“Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.”
—Nadine Gordimer (b. 1923)