Karl L.E.Nickel(1924–2009)∗
J¨u rgen Garloff
Konstanz,Germany
garloff@htwg-konstanz.de
DIE INTERVALLSCHACHTELUNGEN
Es konvergieren Intervall-
Schachtelungen¨u berall.
Nach wen’gen Termen
sieht man schon:
den Fehler
kleiner
Epsi-
海鲜家常菜
lon
ε
Professor Dr.Karl Nickel,one of the founding fathers of interval computa-tions in Germany,died on January1,2009,a couple of weeks before his85th birthday1.
Karl Nickel,professor emeritus of mathematics at the Albert-Ludwigs-Univer-sit¨a t in Freiburg,Germany,was born in1924in T¨u bingen.As with most young people of his age,he had tofight in the war.After being relead as a prisoner-of-war,he enrolled at the famous G¨o ttingen University.Following study at G¨o ttingen and T¨u bingen,he received his Diploma in Mathematics(equivalent to a Master’s Degree)in1948.He worked at the Universities of T¨u bingen and Stuttgart and earned the degree of Doctor in Mathematics(equivalent to a PhD)in1949.He was employed in aircraft design in Cordoba,Argentina, between1951–55and worked at the Universities of Brunswick and Karlsruhe between1955–62.As early as1958he gave a cour in a programming language, a novelty at that time;cf.[18].He joined the Faculty of Mathematics at the University of Karlsruhe as a full professor for numerical mathematics and main-frame computing in1962and rve
d there for veral years as director of the Institute of Applied Mathematics.There he was thefirst director both of the Institute of Practical Mathematics and of the Institute for Computer Science, which he founded.Through the activities he played a prominent role in the ri of computer science and in the establishment of education in this subject at Karlsruhe.In1976he moved to the University of Freiburg,where he rved
62Karl L.E.Nickel(1924–2009) as director of the Institute of Applied Mathematics for many years until his retirement in1989.
舟山定海Professor Nickel began his academic career with papers on the solution of aerodynamic problems and his fundamental works on boundary layer theory. With his early paper“¨Uber die Notwendigkeit einer Fehlerschranken-Arithmetik f¨u r Rechenautomaten”,Numer.Math.9(1966),pp.69–79,he became thefirst rearcher in Germany to work on interval computations.He wrote over40 papers on interval mathematics and related problems,focussing on one of the first programming languages which supported interval computations(Triplex-ALGOL60)[2,4],on enclosing zeros of polynomials[1,5,6],the Newton method[8,14],the centred form[15],numerical integration with error bounds [3],the summation method of Kahan-Babuˇs ka[7],the Prae-Euler summation method[17],stability and convergence of numerical and monotone algorithms [9,11,12],and the lattice-
theoretical foundation of interval analysis[10].He also contributed to the guaranteed numerical solution of ordinary differential ,[13],and to the solution of systems of linear interval equations, e.g.,[16].
Professor Nickel founded the“Interval Library”at the University of Karl-sruhe which was continued at the University of Freiburg and grew to over2000 contributions from interval mathematics and relatedfields2.This library rep-rents a comprehensive archive of the interval computation literature from the beginning of the subject to about1988.Prof.Nickel also was the founder and editor of thefirst interval-related journal“Freiburger Intervall-Berichte”which was published between1978–87.He organid three international conferences on interval mathematics:one at the University of Karlsruhe in1975[19]and two at the University of Freiburg in1980[21]and1985[22].He was also the founder and chairman of the GAMM committee for interval mathematics.
Through the activities Professor Nickel contributed enormously to the propagation of the ideas of interval mathematics.He was an enthusiastic teacher, being an advisor to26doctoral disrtations and97masters’thes.He was a member of the“Deutsche Akademie der Naturforscher Leopoldina”and of the Academy of Creative Endeavours(Akademija Twortschestwa)of the former USSR as well as an honorary professor of Liaoning University in Shenyang/ Liaoning,China.
Over the years,Professor Nickel never lost his interest in aeronautics.Since the early1980’s he expended much effort on the design of ultralight airplanes. With his PhD student M.Wohlfahrt he wrote a book on tailless airplanes[24]; not only did he design planes,he was also an enthusiastic motor glider pilot.
During his life he wrote poems.They appeared under the pudonym KLEN in Palmstr¨o m als Programmierer[20]in the tradition of the Galgen-lieder(Gallows Songs),Palmstr¨o m,Palma Kunkel,Der Ginganz by the Ger-man poet Christian Morgenstern(1871–1914).Under this pudonym he also collected Sch¨u ttelspr¨u che[25]and wrote an introduction to the construction of
Reliable Computing14,201063 Sch¨u ttelreime[23],a kind of(often humorous)rhyming.
The poem on the convergence of nested interval quences at the beginning of this obituary and the one given below are taken from[20],pp.16and46.
DAS STUMMSCHE KONSOL
Stumm erfindet ein Konsol,
das gleich zweifach Werte zeigt,
sich zur ob’ren Grenz’sowohl,
als auch zum Infimum neigt.
Rundungsfehler oder Daten-,
计算机科学与技术
Fehler bei der Konversion
aufgefangen(’s gibt kein Raten),
auch die Abbrechfehler schon.
Denn bei dem Konsol von Stumm
mit dem Doppelzahlenpaar
(ihm ist:“N¨a herung”zu dumm)若干名是什么意思
ist’s Ergebnis wirklich wahr.
J¨u rgen Garloff
Selected publications by Karl Nickel:
Papers and reports:
[1]Die numerische Berechnung der Wurzeln eines Polynoms,Numer.Math.
9(1966),pp.80–98.
[2]The algorithmic language Triplex-ALGOL-60,Numer.Math.11(1968),
pp.175–180(jointly with N.Apostolatos,R.Krawczyk,U.Kulisch,B.
Lortz,and H.-W.Wippermann).
[3]Quadraturverfahren mit Fehlerschranken,Computing3(1968),pp.47–64.
[4]Triplex-Algol with applications,in:Hann,E.(ed),Topics in Interval
厌食症怎么得上的Analysis,Oxford University Press,1969,pp.10–24.
[5]Zeros of polynomials and other topics,in:Hann,E.(ed),Topics in
活动内容怎么写
Interval Analysis,Oxford University Press,1969,pp.25–34.
[6]Fehlerschranken zu N¨a herungswerten von Polynomwurzeln,Computing6
(1970),pp.9–27.
64Karl L.E.Nickel(1924–2009) [7]Das Kahan-Babuˇs kasche Summierungsverfahren in Triplex-ALGOL60,Z.
Angew.Math.Mech.50(1970),pp.369–373.
[8]On the Newton Method in Interval Analysis,MRC Tech.Summary Rep.
#1136,University of Wisconsin,Madison,1971.
[9]Termination criterion and numerical convergence,SIAM J.Numer.Anal.
9(1972),pp.277–283(jointly with K.Ritter).
[10]Verbandstheoretische Grundlagen der Intervall-Mathematik,in[19],pp.
251–262.
[11]¨Uber die Stabilit¨a t und Konvergenz numerischer Algorithmen,Computing
15(1975),part I:pp.291–309,part II:pp.311–328.
南瓜什么时候种植
[12]Stability and convergence of monotonic algorithms,J.Math.Anal.Appl.
爱跳舞的女孩54(1976),pp.157–172.
[13]The construction of a priori bounds for the solution of a two point bound-
ary value problem withfinite elements I,Computing23(1979),pp.247–
265.
[14]A globally convergent ball Newton method,SIAM J.Numer.Anal.18
(1981),pp.988–1003.
[15]Die zentrische Form in der Intervallarithmetik,ihre quadratische Kon-
vergenz und ihre Inklusionsisotonie,Computing28(1982),pp.117–137
(jointly with R.Krawczyk).
[16]Die Au߬o sbarkeit linearer Kreisscheiben-und Intervall-Gleichungssysteme,
Linear Algebra and Appl.44(1982),pp.19–40.
[17]Das Prae-Eulersche Limitierungsverfahren,Z.Angew.Math.Mech.63
(1983),pp.465–478.
Books:
[18]ALGOL-Praktikum.Eine Einf¨u hrung in das Programmieren,G.Braun
Verlag,Karlsruhe,1964(2nd ed.:1971).
[19]Interval Mathematics,ed,Lect.Notes Comp.Sci.,Vol.29,Springer
Verlag,Berlin,Heidelberg,1975.
[20]Palmstr¨o m als Programmierer,Carl Hanr Verlag,Munich,Vienna,1977.
[21]Interval Mathematics1980,ed,Academic Press,New York,London,Toronto,
1980.
[22]Interval Mathematics1985,ed,Lect.Notes Comp.Sci.,Vol.212,
Springer Verlag,Berlin,Heidelberg,1986.
[23]Sch¨u ttelreime lbst gemacht,Verlag Lax,Hildesheim,1987.
Reliable Computing14,201065 [24]Schwanzlo Flugzeuge,Birkh¨a ur Verlag,Bal,Boston,Berlin,1990;
English translation:Tailless Aircraft in Theory and Practice,American Institute of Aeronautics and Astronautics(AIAA),Washington,DC,and Edward Arnold,UK(jointly with M.Wohlfahrt).
[25]Sch¨u ttelspr¨u che,Eine Anthologie,Verlag Lax,Hildesheim,1995.
