Alan Turing and the origins of modern Gaussian elimination

206 Pages·2012·1.39 MB·English

by  Froilán M. Dopico

Alan Turing and the origins of modern
Gaussian elimination
Froilán M. Dopico
DepartamentodeMatemáticasand
InstitutodeCienciasMatemáticasCSIC-UAM-UC3M-UCM,
UniversidadCarlosIIIdeMadrid,Spain
International Symposium: The Alan Turing Legacy.
Madrid, Spain, October 23-24, 2012
F.M.Dopico (ICMAT-U.CarlosIII,Madrid) TuringandGaussianelimination Symposium:TuringLegacy 1/62
My scientific connection with Alan Turing (I)
Ioftenteachagraduatecourse
on “Numerical Linear Alge-
bra”, that is my research area,
andN.Higham, “Accuracyand
Stability of Numerical Algo-
rithms”, (SIAM,2002)isoneof
my favorite references for this
course.
F.M.Dopico (ICMAT-U.CarlosIII,Madrid) TuringandGaussianelimination Symposium:TuringLegacy 2/62
My scientific connection with Alan Turing (II)
Nicholas Higham (1961-) is a
prominent numerical analyst,
who is Richardson Professor
of Applied Mathematics in the
School of Mathematics at Alan
Turing Building in The Univer-
sityofManchester.
Turingspentthelastpartofhis
life (1948-1954) at The Univer-
sityofManchester.
F.M.Dopico (ICMAT-U.CarlosIII,Madrid) TuringandGaussianelimination Symposium:TuringLegacy 3/62
My scientific connection with Alan Turing (III)
NickHigham’sbookisdedicatedtoAlanTuringandJamesWilkinson
AlanTuring(1912-1954) JamesWilkinson(1919-1986)
F.M.Dopico (ICMAT-U.CarlosIII,Madrid) TuringandGaussianelimination Symposium:TuringLegacy 4/62
My scientific connection with Alan Turing (IV)
Thestandardmethodforsolvingsystemsoflinearequationsina
computerisGaussianelimination,
which is one of the most important numerical algorithms!!!
ItisstudiedindepthinChapter9ofNickHigham’s,“Accuracyand
StabilityofNumericalAlgorithms”,wherewefound(pages184-185)
“TheexperiencesofFox,Huskey,andWilkinsonpromptedTuringtowriteare-
markablepaper“Roundingofferrorsinmatrixprocesses”(QuarterlyJour-
nalofMechanicsandAppliedMathematics,1(1948),pp. 287-308)...”
F.M.Dopico (ICMAT-U.CarlosIII,Madrid) TuringandGaussianelimination Symposium:TuringLegacy 5/62
My scientific connection with Alan Turing (IV)
Thestandardmethodforsolvingsystemsoflinearequationsina
computerisGaussianelimination,
which is one of the most important numerical algorithms!!!
ItisstudiedindepthinChapter9ofNickHigham’s,“Accuracyand
StabilityofNumericalAlgorithms”,wherewefound(pages184-185)
“TheexperiencesofFox,Huskey,andWilkinsonpromptedTuringtowriteare-
markablepaper“Roundingofferrorsinmatrixprocesses”(QuarterlyJour-
nalofMechanicsandAppliedMathematics,1(1948),pp. 287-308)...”
F.M.Dopico (ICMAT-U.CarlosIII,Madrid) TuringandGaussianelimination Symposium:TuringLegacy 5/62
My scientific connection with Alan Turing (IV)
Thestandardmethodforsolvingsystemsoflinearequationsina
computerisGaussianelimination,
which is one of the most important numerical algorithms!!!
ItisstudiedindepthinChapter9ofNickHigham’s,“Accuracyand
StabilityofNumericalAlgorithms”,wherewefound(pages184-185)
“TheexperiencesofFox,Huskey,andWilkinsonpromptedTuringtowriteare-
markablepaper“Roundingofferrorsinmatrixprocesses”(QuarterlyJour-
nalofMechanicsandAppliedMathematics,1(1948),pp. 287-308)...”
F.M.Dopico (ICMAT-U.CarlosIII,Madrid) TuringandGaussianelimination Symposium:TuringLegacy 5/62
My scientific connection with Alan Turing (IV)
Thestandardmethodforsolvingsystemsoflinearequationsina
computerisGaussianelimination,
which is one of the most important numerical algorithms!!!
ItisstudiedindepthinChapter9ofNickHigham’s,“Accuracyand
StabilityofNumericalAlgorithms”,wherewefound(pages184-185)
“TheexperiencesofFox,Huskey,andWilkinsonpromptedTuringtowriteare-
markablepaper“Roundingofferrorsinmatrixprocesses”(QuarterlyJour-
nalofMechanicsandAppliedMathematics,1(1948),pp. 287-308)...”
F.M.Dopico (ICMAT-U.CarlosIII,Madrid) TuringandGaussianelimination Symposium:TuringLegacy 5/62
My scientific connection with Alan Turing (IV)
Thestandardmethodforsolvingsystemsoflinearequationsina
computerisGaussianelimination,
which is one of the most important numerical algorithms!!!
ItisstudiedindepthinChapter9ofNickHigham’s,“Accuracyand
StabilityofNumericalAlgorithms”,wherewefound(pages184-185)
“TheexperiencesofFox,Huskey,andWilkinsonpromptedTuringtowriteare-
markablepaper“Roundingofferrorsinmatrixprocesses”(QuarterlyJour-
nalofMechanicsandAppliedMathematics,1(1948),pp. 287-308)...”
F.M.Dopico (ICMAT-U.CarlosIII,Madrid) TuringandGaussianelimination Symposium:TuringLegacy 5/62
My scientific connection with Alan Turing (V)
“Inthispaper,Turingmadeseveralimportantcontributions.
HeformulatedtheLUfactorizationofamatrix... showingthat
GaussianeliminationcomputesanLUfactorization.
Heintroducedthetermconditionnumberanddefinedtwomatrix
conditionnumbers...
Heexploitedbackwarderrorideas...
Finally,andperhapsmostimportantly,heanalysedGaussian
eliminationwithpartialpivotingforgeneralmatrices... andobtained
aboundfortheerror...”
IamnotmentioningallcontributionslistedbyN.Higham.
F.M.Dopico (ICMAT-U.CarlosIII,Madrid) TuringandGaussianelimination Symposium:TuringLegacy 6/62