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The difference between the function $x^n$ and a polynomial spline $S_{n-1}(x)$ of degree $n-1$. Monosplines arise in the study of quadrature formulas for differentiable functions.



[a1] R.S. Johnson, "On monosplines of least deviation" Trans. Amer. Math. Soc. , 96 (1960) pp. 458–477
[a2] I.J. Schoenberg, "Monosplines and quadrature formulae" T.N.E. Greville (ed.) , Theory and applications of spline functions , Acad. Press (1969) pp. 157–207
[a3] L.L. Schumaker, "Spline functions, basic theory" , Wiley (1981)
[a4] A.A. Zhensykbaev, "Monosplines of minimal norm and the best quadrature formulae" Russ. Math. Surveys , 36 : 4 (1981) pp. 121–180 Uspekhi Mat. Nauk , 36 : 4 (1981) pp. 107–159
[a5] A.A. Zhensykbaev, "On monosplines with nonnegative coefficients" J. Approximation Theory , 55 (1988) pp. 172–182
How to Cite This Entry:
Monospline. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by Yu.N. Subbotin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article