Spline Functions and Multivariate Interpolations pp 109-116 | Cite as
Monosplines
Chapter
Abstract
Functions of the form t r /r! + s(t) where s(t) is a spline of degree r - 1 are called monosplines. To be precise, a monospline of degree r with knots x 1 ... x n of multiplicities v 1,..., v n respectively, is any expression of the form with real coefficients {a j } and {c kα}, 1 ⩽ v k ⩽ r, k = 1, ... n. The interest in monosplines comes from their close relation with quadrature formulae.
$$\frac{{{t^r}}}{{r!}} + \sum\limits_{j = 0}^{r - 1} {{a_j}{t^j} + } \sum\limits_{k = 1}^n {\sum\limits_{\alpha = 0}^{{v_k} - 1} {{c_{k\alpha }}(x - {x_k})_ + ^{r - \alpha - 1}} } $$
Keywords
Quadrature Formula Fundamental Theorem Piecewise Linear Function Algebraic Polynomial Real Coefficient
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information
© Springer Science+Business Media Dordrecht 1993