This book constitutes the thoroughly refereed post-proceedings of the Third International Conference on Large-Scale Scientific Computing, LSSC 2001, held in Sozopol, Bulgaria, in June 2001.The 7 invited full papers and 45 selected revised papers were carefully reviewed for inclusion in the book. The papers are organized in topical sections on robust preconditioning algorithms, Monte-Carlo methods, advanced programming environments for scientific computing, large-scale computations in air pollution modeling, large-scale computations in mechanical engineering, and numerical methods for incompressible flow.

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-NystromIntegrationMethods . . 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-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-NystromIntegrationMethods . . 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 ...

This book constitutes the refereed proceedings of the First International Workshop on Numerical Analysis and Its Applications, WNAA'96, held in Rousse, Bulgaria, in June 1996.
The 57 revised full papers presented were carefully selected and reviewed for inclusion in the volume; also included are 14 invited presentations. All in all, the book offers a wealth of new results and methods of numerical analysis applicable in computational science, particularly in computational physics and chemistry. The volume reflects that the cooperation of computer scientists, mathematicians and scientists provides new numerical tools for computational scientists and, at the same time, stimulates numerical analysis.