• 数值最优化
  • 数值最优化
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数值最优化

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作者劳斯特 著

出版社科学出版社

出版时间2006-12

版次1

装帧精装

上书时间2024-11-14

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图书标准信息
  • 作者 劳斯特 著
  • 出版社 科学出版社
  • 出版时间 2006-12
  • 版次 1
  • ISBN 9787030166753
  • 定价 98.00元
  • 装帧 精装
  • 开本 其他
  • 纸张 胶版纸
  • 页数 664页
  • 字数 779千字
  • 正文语种 简体中文,英语
  • 原版书名 Numerical Optimization
【内容简介】
  本书提供优化中大多数有效方法的全面的最新的论述。每一章从基本概念开始,逐步阐述当前可用的最佳技术。
【作者简介】
作者:(美国)劳斯特(Jorge Nocedal)
【目录】
PartIProblemsandTricks
1ElementaryNumberTheory
1.1ProblemsAboutPrimes.DivisibilityandPrimality
1.2DiophantineEquationsofDegreeOneandTwo
1.3CubicDiophantineEquations
1.4ApproximationsandContinuedFractions
1.5DiophantineApproximationandtheIrrationality
2SomeApplicationsofElementaryNumberTheory
2.1FactorizationandPublicKeyCryptosystems
2.2DeterministicPrimalityTests
2.3FactorizationofLargeIntegers
PartIIIdeasandTheories
3InductionandRecursion
3.1ElementaryNumberTheoryFromthePointofViewofLogic
3.2DiophantineSets
3.3PartiallyRecursiveFunctionsandEnumerableSets
3.4DiophantinenessofaSetandalgorithmicUndecidability
4Arithmeticofalgebraicnumbers
4.1AlgebraicNumbers:TheirRealizationsandGeometry
4.2DecompositionofPrimeIdeals,DedekindDomains,andValuations
4.3LocalandGlobalMethods
4.4ClassFieldTheory
4.5GaloisGroupinAritheticalProblems
5Arithmeticofalgebraicvarieties
5.1ArithmeticVarietiesandBasicNotionsofAlgebraicGeometry
5.2GeometricNotionsintheStudyofDiophantineequations
5.3Ellipticcurves,AbelianVarieties,andLinearGroups
5.4DiophantineEquationsandGaloisRepressentations
5.5TheTheoremofFaltingsandFinitenessProblemsinDiophantineGeometry
6ZetaFunctionsandModularForms
6.1ZetaFunctionsofArithmeticSchemes
6.2L-Functions,theTheoryofTateandExpliciteFormulae
6.3ModularFormsandEulerProducts
6.4ModularFormsandGaloisRepresentations
6.5AutomorphicFormsandTheLanglandsProgram
7FermatsLastTheoremandFamiliesofModularForms
7.1Shimura-Taniyama-WeilConjectureandReciprocityLaws
7.2TheoremofLanglands-TunnellandModularityModulo3
7.3ModularityofGaloisrepresentationsandUniversalDeformationRings
7.4WilesMainTheoremandIsomorphismCriteriaforLocalRings
7.5WilesInductionStep:ApplicationoftheCriteriaandGaloisCohomology
7.6TheRelativeInvariant,theMainInequalityandTheMinimalCase
7.7EndofWilesProofandTheoremonAbsoluteIrreducibility
PartIIIAnalogiesandVisions
III-0IntroductorysurveytopartIII:motivationsanddescription
III.1Analogiesanddifferencesbetweennumbersandfunctions:8-point,Archimedeanpropertiesetc.
III.2Arakelovgeometry,fiberover8,cycles,Greenfunctions(dapresGillet-Soule)
III.3-functions,localfactorsat8,SerresT-factors
III.4Aguessthatthemissinggeometricobjectsarenoncommutativespaces
8ArakelovGeometryandNoncommutativeGeometry
8.1SchottkyUniformizationandArakelovGeometry
8.2CohomologicalConstructions
8.3SpectralTriples,DynamicsandZetaFunctions
8.4Reductionmod8
References
Index
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