Applied Numerical Linear Algebra

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

2、........31.3.2PerturbationTheoryandConditionNumbers......41.3.3E®ectsofRoundo®ErroronAlgorithms.........41.3.4AnalyzingtheSpeedofAlgorithms............51.3.5EngineeringNumericalSoftware.............61.4Example:PolynomialEvaluation.................71.5FloatingPoint

3、Arithmetic.....................91.6PolynomialEvaluationRevisited.................151.7VectorandMatrixNorms.....................191.8ReferencesandOtherTopicsforChapter1...........231.9QuestionsforChapter1......................242LinearEquationSolving312.1Introducti

4、on.............................312.2PerturbationTheory........................322.2.1RelativePerturbationTheory...............352.3GaussianElimination........................382.4ErrorAnalysis...........................442.4.1TheNeedforPivoting...................4

5、52.4.2FormalErrorAnalysisofGaussianElimination.....462.4.3EstimatingConditionNumbers..............502.4.4PracticalErrorBounds..................542.5ImprovingtheAccuracyofaSolution..............602.5.1SinglePrecisionIterativeRe¯nement...........612.5.2Equilibration

6、........................622.6BlockingAlgorithmsforHigherPerformance..........632.6.1BasicLinearAlgebraSubroutines(BLAS)........652.6.2HowtoOptimizeMatrixMultiplication.........672.6.3ReorganizingGaussianEliminationtouseLevel3BLAS722.6.4MoreAboutParallelismandOther

7、PerformanceIssues.752.7SpecialLinearSystems.......................762.7.1RealSymmetricPositiveDe¯niteMatrices........76vvi2.7.2SymmetricInde¯niteMatrices..............792.7.3BandMatrices.......................792.7.4GeneralSparseMatrices..................832.7.5De

8、nseMatricesDependingonFewerThanO(n2)Pa-rameters...........................902.8ReferencesandOtherTopicsforChapter2...........922.9QuestionsforChapter2..