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)
“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.”
—Adrienne Rich (b. 1929)
“According to our social pyramid, all men who feel displaced racially, culturally, and/or because of economic hardships will turn on those whom they feel they can order and humiliate, usually women, children, and animals—just as they have been ordered and humiliated by those privileged few who are in power. However, this definition does not explain why there are privileged men who behave this way toward women.”
—Ana Castillo (b. 1953)