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Abstract

An abbreviation of basis spline, introduced in Schoenberg (1967): A chain of polynomials of fixed degree (usually cubic functions are used) ordered in such a way that they are continuous at the points at which they join (knots). The knots are usually placed at the x- coordinates of the data points. The function is fitted in such a way that it has continuous first- and second-derivatives at the knots; the second derivative can be set to zero at the first and last data points. Splines were first described by the Romanian-American mathematician, Isaac Jacob Schoenberg (1903–1990) (Schoenberg 1946, 1971). Other types include: quadratic, cubic and bicubic splines (Ahlberg et al. 1967). Jupp (1976) described an early application of B-splines in geophysics. See also: piecewise function, spline, smoothing spline regression.

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Howarth, R.J. (2017). B. In: Dictionary of Mathematical Geosciences . Springer, Cham. https://doi.org/10.1007/978-3-319-57315-1_2

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