Computational Interdisciplinary Graduate Programs (CIGP) CS&E/CLS Distinguished Seminar Wednesday, April 13, 2016 at 3:30 p.m. in LWSN 1142 WALTER GAUTSCHI Professor Emeritus of Computer Science and Mathematics “A DISCRETE TOP-DOWN MARKOV PROBLEM IN APPROXIMATION THEORY” ABSTRACT BIOGRAPHICAL The Markov brothers’ inequalities in Before coming to Purdue, Professor Gautschi did postdoctoral work as approximation theory concern a Janggen-Pöhn Research Fellow at the National Institute of Applied polynomials p of degree n and assert Mathematics in Rome and at the Harvard Computation Laboratory. He bounds for the kth derivatives |p(k)|, 1 ≤ also held positions at the National Bureau of Standards, the American k ≤ n, on [−1, 1], given that |p| ≤ 1 on [−1, University, the Oak Ridge National Laboratory, and the University of 1]. Here we go the other direction, Tennessee. Since coming to Purdue, he has been a Fulbright Scholar seeking bounds for |p|, given a bound at the Technical University of Munich and has held visiting for |p(k)|. For the problem to be appointments at the University of Wisconsin, Argonne National meaningful, additional restrictions on p Laboratory, the Wright-Patterson Air Force Base, ETH Zurich, the must be imposed, for example, p(−1) = University of Padova, and the University of Basel. He has been a p′(−1) = · · · = p(k−1) = 0. The problem Fulbright Lecturer, an ACM National Lecturer, and a SIAM Visiting then has an easy solution in the Lecturer. He is, or has been, on the editorial boards of SIAM Journal continuous case, where the polynomial on Mathematical Analysis, Numerische Mathematik, Calcolo, and and their derivatives are considered on Mathematics of Computation, and has served as a special editor for the whole interval [−1, 1], but is more Linear Algebra and Its Applications. From 1984 to 1995, he was the challenging, and also of more interest, in managing editor of Mathematics of Computation and, since 1991, an the discrete case, where one focusses on honorary editor of Numerische Mathematik. In 2001, Professor the values of p and pk) on a given set of Gautschi was elected a Corresponding Member of the Bavarian n distinct points in [−1, 1]. Two analytic Academy of Sciences and Humanities and, in the same year, a Foreign solutions are presented and their fine Member of the Academy of Sciences of Turin. structure analyzed by computation. [email protected] CIGP, Office of Interdisciplinary Graduate Programs. B40 YONG, 155 S. Grant St. West Lafayette, IN 47907. TEL:(765) 494-0379, Email: [email protected] .