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1、SparseMatrixTechnologySparseMatrixTechnologySergioPissanetzkyCentroAt6micoBariloche,Bariloche,Argentina1984ACADEMICPRESS(HarcourtBraceJovanovich,Publishers)LondonOrlandoSanDiegoSanFranciscoNewYorkTorontoMontrealSydneyTokyoSaoPauloAllRightsReservedNopartofthisbookmaybereproducedinanyfo
2、rmbyphotostat,microfilm,oranyothermeans,withoutwrittenpermissionfromthepublishersTypesetby.EtaServices(Typesetters)LtdandprintedinGreatBritainbyThomsonLitho,EastKilbride.PrefaceAscomputersgrowinpowerandspeed,matricesgrowinsize.In1968,practicalproductioncalculationswithlinearalgebraics
3、ystemsoforder5000werecommonplace,whilea"large"systemwasoneoforder10000ormore.1In1978,anoverdeterminedproblemwith2.5millionequationsin400000unknownswasreported/in1981,themagnitudeofthesameproblemhadgrown:ithad6000000equations,stillin400000unknowns.3Thematrixofcoefficientshad2.4x1012ent
4、ries,mostofwhichwerezero:itwasasparsematrix.Asimilartrendtowardincreasingsizeisobservedineigenvaluecalculations,wherea"large"matrixisoneoforder4900or12000.4Willmatrixproblemscontinuetogrowevenfurther?Willourabilitytosolvethemincreaseatasufficientlyhighrate?Butthisisonlyonesideoftheque
5、stion.Theothersideconcernsthemicrocomputerexplosion.Microcomputersnowhaveaboutthesamepoweraslargecomputershadtwodecadesago.Areusersconstrainedtosolvingmatrixproblemsofthesamesizeasthoseoftwentyyearsago?Theownerofamicrocomputermaynotcaretoomuchaboutthecostofcomputation;themaindifficult
6、yisstorage.Onalargemachine,thecostofsolvingamatrixproblemincreasesrapidlyifthesizeoftheproblemdoes,becausebothstorageandlabourgrow.Theoverallcostbecomesaprimaryconsideration.Howcansuchcostbeminimizedforagivenproblemandinstallation?Answerstotheseandotherrelatedquestionsaregiveninthisbo
7、okforthefollowingclassesofmatrixproblems:directsolutionofsparselinearalgebraicequations,solutionofsparsestandardandgeneralizedeigenvalueproblems,andsparsematrixalgebra.Methodsaredescribedwhichrangefromverysimpleyetsurprisinglyeffectiveideastohighlysophisticatedalgorithms.Sparsematrixt
8、echno
