Numerical analysis and its applications

de Lubin Vulkov

ThisvolumeoftheLectureNotesinComputerScienceseriescontainsthep- ceedings of the Second Conference on Numerical Analysis and Applications, which was held at the University of Rousse, Bulgaria, June 11-15,2000. The conferencewasorganizedbytheDepartmentofNumericalAnalysisandStat- ticsattheUniversityofRoussewithsupportfromtheUniversityofSouthern Mississippi, Hattiesburg. The conference was co-sponsored by SIAM (Society for Industrial and Applied Mathematics) and ILAS (International Linear - gebra Society). The o?cial sponsors of the conference were Fujitsu America, Inc. ,Hewlett-PackardGmbH,andSunMicrosystems. Wewouldliketogiveour sincerethankstoallsponsorsandco-sponsorsforthetimelysupport. The second conference continued the tradition of the ?rst one (1996 in Rousse) as a forum, where scientists from leading research groups from the “East” and “West” are provided with the opportunity to meet and exchange ideasandestablishresearchcooperation.^ Morethan120scientistsfrom31co- triesparticipatedintheconference. Awiderangeofproblemsconcerningrecentachievementsinnumericalan- ysisanditsapplicationsinphysics,chemistry,engineering,andeconomicswere discussed. An extensiveexchangeofideasbetweenscientists whodevelopand studynumericalmethodsandresearcherswhousethemforsolvingreal-lifepr- lemstookplaceduringtheconference. Weareindebtedtoourcolleagueswhohelpedusintheorganizationofthis conference. Wethanktheorganizersofthemini-symposiaforattractingactive andhighlyquali?edresearchers. October2000 LubinVulkov JerzyWa´sniewski PlamenYalamov Table of Contents Numerical Analysis and Its Applications SensitivityAnalysisoftheExpectedAccumulatedReward UsingUniformizationandIRK3Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 H. Abdallah andM. Hamza SpectralPropertiesofCirculantBandMatricesArisinginODEMethods . . . 10 P. Amodio AParameterRobustMethodforaProblemwith aSymmetryBoundaryLayer . . . . . . . . . . . . . . .^ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 A. R. Ansari,A. F. HegartyandG. I. Shishkin AnAlgorithmBasedonOrthogonalPolynomialVectors forToeplitzLeastSquaresProblems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 M. VanBarel, G. Heinig andP. Kravanja FromSensitivityAnalysistoRandomFloatingPointArithmetics– ApplicationtoSylvesterEquations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 A. Barraud, S. LesecqandN. Christov ConstructionofSeminumericalSchemes: ApplicationtotheArti?cialSatelliteProblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 R. Barrio StabilityAnalysisofParallelEvaluationofFiniteSeries ofOrthogonalPolynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 R. Barrio andP. Yalamov OnSolvingLarge-ScaleWeightedLeastSquaresProblems. . . . . . . . . . . . . . . . . . 59 V.^ Baryamureeba AHybridNewton-GMRESMethodforSolvingNonlinearEquations . . . . . . . 68 S. Bellavia, M. Macconi andB. Morini ComparativeAnalysisofMarchingAlgorithms forSeparableEllipticProblems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 G. Bencheva InexactNewtonMethodsandMixedNonlinearComplementaryProblems . . 84 L. Bergamaschi and G. Zilli Skew-CirculantPreconditionersforSystemsofLMF-BasedODECodes . . . . 93 D. Bertaccini andM. K. Ng NewFamiliesofSymplecticRunge–Kutta–Nystr¨omIntegrationMethods . . 102 S. Blanes, F. Casas andJ. Ros VIII Table ofContents ConvergenceofFiniteDi?erenceMethodforParabolicProblem withVariableOperator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 D. Bojovi´ c FiniteVolumeDi?erenceSchemefor aSti?EllipticReaction-Di?usionProblemwithaLineInterface . . . . . . . . . . 117 I. A. Braianov Nested-DissectionOrderingsforSparseLUwithPartialPivoting. . . . . . .^ . . . 125 I. Brainman andS. Toledo FractionalStepRunge–KuttaMethodsfortheResolutionof TwoDimensionalTimeDependentCoe?cient Convection–Di?usionProblems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 B. Bujanda andJ. C. Jorge VariableStepsizesinSymmetricLinearMultistepMethods. . . . . . . . . . . . . . . . 144 B. Cano PreliminaryRemarksonMultigridMethodsforCirculantMatrices . . . . . . . .