Contemporary Computational Mathematics – A Celebration of the 80th Birthday of Ian Sloan Josef Dick (cid:129) Frances Y.Kuo (cid:129) Henryk Woz´niakowski Editors Contemporary Computational Mathematics – A Celebration of the 80th Birthday of Ian Sloan 123 Editors JosefDick FrancesY.Kuo SchoolofMathematicsandStatistics SchoolofMathematicsandStatistics UniversityofNewSouthWales UniversityofNewSouthWales Sydney,Australia Sydney,Australia HenrykWoz´niakowski InstituteofAppliedMathematics andMechanics UniversityofWarsaw Warsaw,Poland DepartmentofComputerScience ColumbiaUniversity NewYork,USA ISBN978-3-319-72455-3 ISBN978-3-319-72456-0 (eBook) https://doi.org/10.1007/978-3-319-72456-0 LibraryofCongressControlNumber:2018936907 Mathematics Subject Classification (2010): 11K38, 41A55, 41A63, 65C05, 65D30, 65D32, 65N30, 65N35,65R20,65R30 ©SpringerInternationalPublishingAG,partofSpringerNature2018 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. Printedonacid-freepaper ThisSpringerimprintispublishedbytheregisteredcompanySpringerInternationalPublishingAGpart ofSpringerNature. Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland DedicatedtoIan H. Sloanontheoccasionof his80thbirthday. Preface On June 17, 2018,Professor Ian Hugh Sloan will celebrate his 80th birthday.We aredelightedinwishinghimwellonthishappyoccasion.Ianhasbeenateacher,a mentor,aresearchcollaborator,andaverydearfriendtomanyofus. We decided to give Ian a special birthday present in the form of this book as a tribute to his many important contributions in various areas of computational mathematics.Atthispoint,wewishtothankthecolleagueswhocontributedtothis bookasauthorsand/orreferees.Infact,theresponseofsendingpaperstocelebrate the80thbirthdayofIanwassogreatandfromsomanycolleaguesthatitwasindeed adifficultjobforustolimitthenumberofpagesofthebook.Weareverygratefulto SpringerVerlagthattheyagreedfromtheverybeginningthatthenumberofpages ofthebookwillnotbeanissue. The book consists of nearly 60 articles written by international leaders in a diverse range of areas in contemporarycomputationalmathematics. These papers highlight impact and many achievements of Ian in his distinguished academic career. The papers also present the current state of knowledge in such areas as quasi-Monte Carlo and Monte Carlo methods for multivariate integration, multi- levelmethods,finiteelementmethods,uncertaintyquantification,sphericaldesigns and integration on the sphere, approximation and interpolation of multivariate functions,andoscillatoryintegralsandingeneralininformation-basedcomplexity andtractability,aswellasinarangeofothertopics. Thisbooktellsanimportantpartofthelifestoryoftherenownedmathematician, familyman,colleague,andfriendwhohasbeenaninspirationtosomanyofus. Webelievethatthebestwaytobeginthisbookisbypresentingafewwordsabout Ian.We arealso surethatthe readerwill enjoyreadingthefamilyperspectiveson Ianbyhiswife Jan,hischildrenJenniandTony,andhisgrandchildrenSam,Gus, Mack,Corrie,andKiara.(GranddaughterElizamissedtheopportunitytocontribute duetotravelling.) IanHughSloanwasbornonJune17,1938,inMelbourne,Australia.Hedidhis schoolingatScotchCollege,Melbourne,andBallaratCollege.ThefatherofIanwas a senior mathematics master at Scotch College and later Principal at Ballarat and apparentlytookgoodcareofthebackgroundonmathematicaleducationofhisson. vii viii Preface ThenIanwas educatedatthe UniversityofMelbourne,wherehe obtainedBSc in 1958inphysicsandBA(hons)in1960inpureandappliedmathematics.Ianmethis futurewifeJanattheUniversityofMelbourne,andtheyweremarriedin1961.He obtainedMSc attheUniversityofAdelaidein1961inmathematicalphysicsfora thesisentitled“IonizationinNebulae”.IanwassupervisedinAdelaidebyProfessor HerbertGreenwhowasoneofAustralia’sfirstprofessorsofmathematicalphysics. It is worth mentioning that Ian completed his master’s degree in record time of 7months.IanreceivedhisPhD in1964attheUniversityofLondonintheoretical physicsbasedonthethesis“ElectronCollisionsbyNeutralandIonizedHelium”and was supervised by renowned mathematical physicist Professor Sir Harrie Massey who worked on the Manhattan Project and at the Australian Woomera Rocket Range. Ian completed his PhD againin record time of just 30 months.Part of his PhDworkinvolvedcomputationsonanearlymainframemachineinManchester. Ian Sloanstarted hisprofessionalcareerasa researchscientist forthe Colonial SugarRefiningCompany,during1964–1965,inMelbourne.Since1965IanSloan has been at the University of New South Wales as a member of the School of Mathematics.HewasappointedLecturerin1965andbecameinvolvedinresearch in theoretical nuclear physics. Ian had a very good start at UNSW and published 10singleauthoredpapersinthefirst5years.HewaspromotedtoSeniorLecturer in1968.Hisresearchfocuswasshiftingfromtheoreticalphysicstoappliedmath- ematics,especiallytowardsnumericalanalysis,firstforintegralequationsrelevant toscatteringtheoryandthento computationalmathematicsmostlyof multivariate integration and approximation. He was promoted to Associate Professor in 1973 andwasappointedtoapersonalChairinMathematicsin1983andthentoScientia Professorin1999.HeservedasHeadoftheSchoolofMathematicsofUNSWfrom 1986to1990andfrom1992to1993. Ian had many visiting positions during his career. He was associated, in particular, with (in alphabetical order) Cornell University, ESI in Vienna, Hong KongPolytechnicUniversity,IBMParis,ICERMinProvidenceintheUSA,King FahdUniversityofPetroleumandMineralsinSaudiArabia,Mittag-LefflerInstitute in Stockholm, Newton Institute at Cambridge, Politecnico di Torino, Technical UniversityofVienna,UniversityofBath,UniversityofMaryland(twosabbaticals 1971–1972 and 1979–1980), University of Stuttgart, and Weierstrass Institute in Berlin. Ian Sloan received many honours and awards during his academic career. In 1993 he was elected a Fellow of the Australian Academy of Science; in 1997 he wasawardedtheANZIAMMedalofthe AustralianMathematicalSociety;during 1998–2000he was the President of the Australian Mathematical Society; in 2001 he receivedthe Australian Academy of Science’s ThomasRanken Lyle Medal; in 2001hewasawardedtheCentenaryMedal;in2002hesharedtheinauguralGeorge SzekeresMedaloftheAustralianMathematicalSocietywithAlfvanderPoortenof MacquarieUniversity;during2003–2007hewasthePresidentoftheInternational CouncilforIndustrialandAppliedMathematics(ICIAM);in2005hereceivedthe Information-Based Complexity (IBC) Prize; in the June 2008 Queen’s Birthday Honours,he was appointedan Officer of the Order of Australia (AO); in 2009he Preface ix becameaFellowoftheSocietyforIndustrialandAppliedMathematics(SIAM);in 2012he became a Fellow of the AmericanMathematicalSociety; and in 2014he waselectedaFellowoftheRoyalSocietyofNewSouthWales(FRSN). Ian Sloan has been serving on editorial boards of many international compu- tational mathematical journals. These include Journal of Integral Equations and Applications(1987–2012),SIAMJournalon Numerical Analysis (1991–1997and 2003–2012),JournalofComplexity(1999–2009asAssociateEditorandsince2009 as Senior Editor), Numerische Mathematik (2004–2014), Advances in Computa- tionalMathematics(2000–2015),ComputationalMethodsinAppliedMathematics (2000–2015),ChineseJournalofEngineeringMathematics(2007–),International Journal of Geomathematics (2011–), International Journal for Mathematics in Industry(2013–),andFoundationsofComputationalMathematics(2015–). Ian Sloan loves to work with other people.The list of his collaboratorsis very impressive,andmanyofthemcontributedpaperstothisbook.HewasaPhDadvisor of Reginald Cahill (1971), John Aarons (1972), Ivan Graham (1980), Stephen Joe (1985), Sunil Kumar (1987), Yi Yan (1989), Thanh Tran (1994), Timothy Langtry (1995), Thang Cao (1995), Yi Zeng (1998, co-supervisor), Josef Dick (2004), Kassem Mustapha (2004, co-supervisor), Benjamin Waterhouse (2007), Paul Leopardi (2007), Jan Baldeaux (2010), Cong Pei An (2011, co-supervisor), JamesNichols(2013),AndrewChernih(2013),YuGuangWang(2015),Alexander Gilbert(current,co-supervisor),andYoshihitoKazashi(current). Ian Sloan has so far published more than 280 peer-reviewed papers in leading journalsoftheoreticalphysicsandcomputationalmathematics,bookchapters,and refereed conference proceedings, as well as one book with Stephen Joe entitled Lattice Methods for Multiple Integrationpublished by OxfordUniversity Press in 1994. His papers cover various areas such as the numerical solution of integral equations, boundary integral equations, numerical integration, interpolation and approximationofmultivariatefunctions,partialdifferentialequationswithrandom coefficients, and information-based complexity and tractability. The list of Ian’s publications is included later in this book. He is one of a select few on the 2001 ThompsonISIlistofhighlycitedauthors. ProfessorIanSloanhasmadeoutstandingcontributionstomathematicalresearch overthe last 50 years. Ian’s impactis felt widely today;the Bencze-Redish-Sloan equation and the Sloan iteration for integral equations (see the article by Thanh Traninthismonograph)havebeennamedafterhim.Furtherkeycontributionswere the introductionof weightedspacesandthe studyof tractabilityand inventingthe component-by-componentconstructionoflatticerules. Asmanyofusknow,Ianlovestotravel.Healmostalwaystravelswithhiswife Jan,anditis sometimeseasier tomeetIanandJanabroadthanin Sydney.He has travelled to all parts of the world giving invited talks on his work really almost everywhere.He ismakingmanyfriendsduringhistripsandhasmanyinteresting, notalwaysmathematical,storiestotellabouthistravels.Moreimportantly,Iandoes notslowdown.Heisasenergeticandactivetodayashewasyearsago.IanSloanis arolemodelandinspirationtohisfriendsandcolleagues. x Preface Inadditiontomostauthorsofthisbookwhoalsoservedasreferees,thefollowing people also served as referees for the book: Michael Feischl, Alexander Gilbert, Juan Gonzalez Criado del Rey, Michael Griebel, Thomas Hou, James Hyman, StephenJoe,PierreLÉcuyer,KlausRitter,RobertSchaback,FrankStenger,Kosuke Suzuki, Mario Ullrich, Clayton Webster, Takehito Yoshiki, and Penchuan Zhang. Wesincerelythankallauthorsandrefereesfortheircontributions. WearealsogratefultoMartinPetersofSpringerVerlagforhisstrongsupportof thisbookfromtheverybeginningandformakingitpossiblethateverycontributor receivesafreecopyofthebook. JosefDick FrancesY.Kuo HenrykWoz´niakowski Family Perspectives Jan Sloan(Wife) The Ian Sloan I know is always in a hurry and never has enough time. There is always a paper to finish, a deadline to meet, someone to see, or something to do. I understand that this started early: he began school a few days after turning four becausehe grewimpatientwatchingotherchildrenthroughthe schoolfence.(His fatherwasamathematicsteacherandatthattimewasahousemasterofaboarding housewhichhappenedtobenexttotheprimaryschool.)Afewyearslater,wespent our honeymoonin Adelaide so that he could put in an appearanceat morningtea in the Math Physics Department, to allow him to complete a master’s degree in twoterms—morningteasatisfiedthe“minimumthree-term”requirement!Thenhe completedaPhDintheoreticalphysicsattheUniversityCollegeLondonintwoand ahalfyears,withhisfinaloralexamtakeninataxi.Theoralinataxiwasbecause hissupervisor,ProfessorSirHarrieMassey,wasinevenmoreofahurry:hewasan importantpersoninthespaceprogrammeatCapeCanaveral(nowCapeKennedy), so was rarely in London—indeedIan saw him only six times during his PhD, or sevenifyoucountthetaxi.Buttherewasanotherreasonforurgency,namely,that IanwantedtofinishhisPhDinsuperfasttime. I believe his PhD experiencemade him exceptionallyself-reliant and indepen- dent.Heneverneedsotherstotellhimwhattodo. AfteramemorabletwoandahalfyearsinLondon,wereturnedtoAustraliafor Iantotakeuparesearchpositioninanindustriallab(towhichheowedsomeloyalty sincetheyhadpaidhimtodothePhDinLondon).Iansaysthisperiodofindustrial research was the most miserable period of his working life, since in reality there wasnothingforhimtodo.(Hisindustrybossallowedhimtogogracefully,saying “Wehavetoacceptthatsomepeoplearenotcutoutforresearch.”)Afteragloomy 10monthsin industrialresearch,he was rescuedby an advertisementfor a casual teaching position at the University of New South Wales. And after more than 50 years,heisstillthere! xi