Spline Interpolation and Best Quadrature Formulae
Part of the Contemporary Mathematicians book series (CM)
The spline interpolation formula. A spline function S(x), of degree k(≧0), having the knots
is by definition a function of the class C k−1 which reduces to a polynomial of degree not exceeding k in each of the n+2 intervals in which the points (1) divide the real axis. The function S(x) is seen to depend linearly on n+k +1 parameters. In [5, Theorem 2, p. 258] are given the precise conditions under which we can interpolate uniquely by S(x) arbitrarily given ordinates at n+k +1 points on the real axis.
$$x_0 < x_1 < \cdots < x_n ,$$
KeywordsQuadrature Formula Spline Function Spline Interpolation Minimal Property Mechanical Quadrature
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