The founder of the Institute, Tiberiu Popoviciu, has obtained some outstanding results:
- introduction of the B-spline functions on nonuniform grids, in 1934, studied in depth, obtaining the (now called) Marsden recurrence identity from 1970, and the (now called) Boehm’s knot insertion formula, from 1980. His pioneering contributions have been recognized at the highest level: they were acknowledged in a paper by C. de Boor and A. Pinkus, and in a subsequent paper of C. de Boor; L.N. Trefethen (Univ. Oxford, Univ. Harvard) included him in the list “Who invented the great numerical algorithms?”,
- introduction of the cardinal spline interpolation on arbitrary knots, in 1941, as acknowledged by I.J. Schoenberg himself, in a paper published in Mathematica, in 1968: “In [1941] Popoviciu uses spline functions directly for the purpose for which they are so eminently suited: the approximation of functions. He introduces spline functions of degree n with arbitrary knots…”
- first use of the modulus of continuity for obtaining estimations for the remainders in approximation formulas, in 1937;
- prefiguration of the de Casteljau algorithm, by considering the alternative computation of the value of the Bernstein polynomial, in 1937;
- generalization of the Leibniz formula for the product of two functions to divided differences, in 1933;
- introduction and study of the convex functions of higher order, in 1933 and 1945;
- …
Tiberiu Popoviciu appears in the select History of Approximation Theory (Technion University, Israel).
