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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.
LAPACK95 is a Fortran 95 interface to the Fortran 77 LAPACK
library. It is relevant for anyone who writes in the Fortran 95
language and needs reliable software for basic numerical linear
algebra. It improves upon the original user-interface to the LAPACK
package, taking advantage of the considerable simplifications that
Fortran 95 allows. LAPACK95 Users' Guide provides an introduction
to the design of the LAPACK95 package, a detailed description of
its contents, reference manuals for the leading comments of the
routines, and example programs
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