Tiberiu Popoviciu

February 16, 1906 (Arad) – October 29, 1975 (Cluj-Napoca).

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Author: Emil Cătinaş
Version: August 25, 2018.

© Emil Cătinaş, Tiberiu Popoviciu Institute of Numerical Analysis

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Tiberiu Popoviciu is one of the greatest Romanian mathematicians. [acad. C. Iacob – link soon]

Tiberiu Popoviciu is the most important mathematician given by Transylvania, after János Bolyai. [acad. C. Iacob – link soon]

Tiberiu Popoviciu has set the foundations of the Numerical Analysis in Romania. [acad. M. Nicolescu – link soon]

Tiberiu Popoviciu has important contributions in the foundation of the Computer Science in Romania (hardware & software):

  • a few years after he was appointed professor at the University from Cluj-Napoca, he founded in 1951 the Institute (initially called Sectia de Matematica), within the Romanian Academy.
    His vision was an Institute where the following fields meet together:
    – Numerical Analysis (theory),
    – Applied Mathematics (in Industry – by contracts),
    – Electronic Computing (by building computers);
  • in 1957 he was approved to change the Institute name into Institutul de Calcul, and to hire top electronic engineers, physicists, who started designing and building computers;
  • in 1959 a first, experimental computer with relays is built: MARICA;
  • in 1963, DACICC-1, is the third electronic computer built in Romania, but the first one with transistors, RAM and a library of mathematical functions; Romania was the 11th country in the world that used transistors in computers;
  • in 1963, he had a decisive contribution in the foundation of the Department of Computer Science of the Faculty of Mathematics (Babes-Bolyai University), and he taught some of the first courses;
  • in 1968, DACICC-200, is the first Romanian computer with OS and compiler, and also with several advanced features; it is the most powerful computer designed and built in Romania [citation to be added];
  • in 1973, together with other personalities (E. Muntean, V. Peteanu) Popoviciu had a decisive contribution in the foundation in Cluj-Napoca of one of the first Highschools in Romania on Computer Science (at the same time with the foundation of the other three, in Bucharest, Timisoara and Iasi);

He appears in the select History of Approximation Theory (Technion University, Israel).

Several Institutions and NGOs bear today his name: this Institute (Institutul de Calcul “Tiberiu Popoviciu”), Liceul de informatica Tiberiu Popoviciu, Asociatia pentru IT Tiberiu Popoviciu, Asociatia pentru Matematica T. Popoviciu, the journal Annals of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and Convexity, the highschool symposiums, national Highschool contests on Computer Science, etc.

He was a brilliant graduate of École Normale Supérieure (Paris), obtaining the PhD title at Université Paris-Sorbonne.

He became corresponding member of the Romanian Academy in 1948, at 42 years age, and full member of the Romanian Academy 13 years later.

He has obtained some important, deep results, from various fields of Mathematics (Numerical Analysis, Approximation Theory, Mathematical Analysis, Algebra): he

  • introduced for the first time (in 1934), the B-spline functions on nonuniform grids (as acknowledged in a paper by C. de Boor and A. Pinkus) and deeply studied them, obtaining the (now called) Marsden recurrence identity from 1970, and the (now called) Boehm’s knot insertion formula, from 1980;
  • introduced for the first time (1941) the cardinal spline interpolation on arbitrary knots, as acknowledged by I.J. Schoenberg himself, in a paper from 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…”
  • used for the first time the modulus of continuity for obtaining estimations for the remainders in approximation formulas (1937);
  • prefigured the de Casteljau algorithm (1937);
  • obtained early contributions to the test functions criterion for the convergence of linear positive operators (1950) – some call it the Bohman-Korovkin-Popoviciu theorem;
  • generalized the Leibniz formula for the product of two functions to divided differences (1933);
  • introduced and studied the convex functions of higher order (1933);
  • obtained a mean value formula for the divided differences of a function;
  • obtained further results on interpolation, quadrature, etc.;
  • obtained inequalities that bear his name (on variances, on convex functions, and others);
  • obtained results in functional equations, algebra (regarding the number of partitions of n)
  • published the first monograph in Romania regarding Numerical Analysis and Approximation Theory (1937);
  • (to be completed)

He is the founder of the Institute of Numerical Analysis (1951) also named the Computing Institute, which now bears his name (in Romanian Institutul de Calcul “Tiberiu Popoviciu”)

He was a visionary mathematician, and foreseen the increasing importance of the numerical computing. He had a vision, which he fulfilled, regarding the Numerical Computing (Numerical Analysis), the Practical Computing (Applied and Industrial Mathematics) and the Electronic Computing. In Romanian, “Calcul” may be associated to all the three mentioned notions

  • Numerical Analysis (“calcul numeric”),
  • Practical/Industrial Mathematics (“calcul practic”) – over 100 contracts with economic agents were carried out using the computers built here;
  • Electronic Computing technique (“calcul electronic”), three electronic computers were built here. The third computer was designed to support hardware implemented instructions for floating point computations (real numbers represented in floating point arithmetic on 48 bits).

The mathematicians from the Institute and from the Babes-Bolyai University, together with their PhD students, and the PhD students of their PhD students,… formed a powerful team, called the Cluj-Napoca Team on Numerical Analysis and Approximation Theory (“Şcoala Clujeană de analiză numerică şi teoria aproximării”), known not only in Romania, but also abroad. It amounts to over 400 people.

The specialists formed at the hardware section of the Institute were transferred in 1968 and formed the Institute for Computers – Cluj (Institutul pentru Tehnică de Calcul – ITC Cluj) and the Territorial Center for Computing (Centrul Teritorial de Calcul Cluj).

The IT industry in Cluj-Napoca has started from Tiberiu Popoviciu. However, it is worth noting that, according to Gh. Farkas, one of the leading engineers of the Institute, Popoviciu has risked his future when engaging the whole Institute resources for constructing some computers they wouldn’t know if would work…