图灵数学·统计学丛书10-应用数值线性代数【英文版暂代】-[美]j·w·戴梅尔-siam出版-1997

《图灵数学·统计学丛书10-应用数值线性代数【英文版暂代】-[美]j·w·戴梅尔-siam出版-1997》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、AppliedNumericalLinearAlgebra应用数值线性代数ٛDemmel.WJames］美［ٛ著SIAM1997Contents1Introduction11.1BasicNotation...........................11.2StandardProblemsofNumericalLinearAlgebra........11.3GeneralTechniques.........................21.3.1MatrixFactorizations...................31.3.2PerturbationTheo

2、ryandConditionNumbers......41.3.3E®ectsofRoundo®ErroronAlgorithms.........41.3.4AnalyzingtheSpeedofAlgorithms............51.3.5EngineeringNumericalSoftware.............61.4Example:PolynomialEvaluation.................71.5FloatingPointArithmetic.....................91.6PolynomialEvaluationRevis

3、ited.................151.7VectorandMatrixNorms.....................191.8ReferencesandOtherTopicsforChapter1...........231.9QuestionsforChapter1......................242LinearEquationSolving312.1Introduction.............................312.2PerturbationTheory........................322.2.1Relat

4、ivePerturbationTheory...............352.3GaussianElimination........................382.4ErrorAnalysis...........................442.4.1TheNeedforPivoting...................452.4.2FormalErrorAnalysisofGaussianElimination.....462.4.3EstimatingConditionNumbers..............502.4.4PracticalErrorB

5、ounds..................542.5ImprovingtheAccuracyofaSolution..............602.5.1SinglePrecisionIterativeRe¯nement...........612.5.2Equilibration........................622.6BlockingAlgorithmsforHigherPerformance..........632.6.1BasicLinearAlgebraSubroutines(BLAS)........652.6.2HowtoOptimizeMat

6、rixMultiplication.........672.6.3ReorganizingGaussianEliminationtouseLevel3BLAS722.6.4MoreAboutParallelismandOtherPerformanceIssues.752.7SpecialLinearSystems.......................762.7.1RealSymmetricPositiveDe¯niteMatrices........76vvi2.7.2SymmetricInde¯niteMatrices..............792.7.3BandMa

7、trices.......................792.7.4GeneralSparseMatrices..................832.7.5DenseMatricesDependingonFewerThanO(n2)Pa-rameters...........................902.8ReferencesandOtherTopicsforChapter2...........922.9QuestionsforChapter2..