数值最优化

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