A geometric proof for the variation diminishing property of B-spline approximation is given. The proof is based primarily upon a generalized form of the de Boor-Cox algorithm and the intuitively obvious fact that piecewise linear interpolation is variation diminishing. Previous proofs [4, 8] employed the mathematical methods of total positivity, a machinery which is available only after reading . © 1983.
Lane, J. M., & Riesenfeld, R. F. (1983). A geometric proof for the variation diminishing property of B-spline approximation. Journal of Approximation Theory, 37(1), 1–4. https://doi.org/10.1016/0021-9045(83)90111-9