矩阵计算

1MatrixMultiplicationProblems

1.1BasicAlgorithmsandNotation

1.2ExploitingStructure

1.3BlockMatricesandAlgorithms

1.4VectorizationandRe-UseIssues

2MatrixAnalysis

2.1BasicIdeasfromLinearAlgebra

2.2VectorNorms

2.3MatrixNorms

2.4FinitePrecisionMatrixComputations

2.5OrthogonalityandtheSVD

2.6ProjectionsandtheCSDecomposition

2.7TheSensitivityofSquareLinearSystems

3GeneralLinearSystems

3.1TriangularSystems

3.2TheLUFactorization

3.3RoundoffAnalysisofGaussianElimination

3.4Pivoting

3.5ImprovingandEstimatingAccuracy

4SpecialLinearSystems

4.1TheLDMTandLDLTFactorizations

4.2PositiveDefiniteSystems

4.3BandedSystems

4.4SymmetricIndefiniteSystems

4.5BlockSystems

4.6VandermondeSystemsandtheFFT

4.7ToeplitzandRelatedSystems

5OrthogonalizationandLeastSquares

5.1HouseholderandGivensMatrices

5.2TheQRFactorization

5.3TheFullRankLSProblem

5.4OtherOrthogonalFactorizations

5.5TheRankDeficientLSProblem

5.6WeightingandIterativeImprovement

5.7SquareandUnderdeterminedSystems

6ParallelMatrixComputations

6.1BasicConcepts

6.2MatrixMultiplication

6.3Factorizations

4SpecialLinearSystems

4.1TheLDMwandLDLwFactorizations

4.2PositiveDefiniteSystems

4.3BandedSystems

4.4SymmetricIndefiniteSystems

4.5BlockSystems

4.6VandermondeSystemsandtheFFT

4.7ToeplitzandRelatedSystems

5OrthogonalizationandLeastSquares

5.1HouseholderandGivensMatrices

5.2TheQRFactorization

5.3TheFullRankLSProblem

5.4OtherOrthogonalFactorizations

5.5TheRankDeficientLSProblem

5.6WeightingandIterativeImprovement

5.7SquareandUnderdeterminedSystems

6ParallelMatrixComputation

6.1BasicConcepts

6.2MatrixMultiplication

6.3Factorizations

7TheUnsymmetricEigenvalueProblem

7.1PropertiesandDecompositions

7.2PerturbationTheory

7.3PowerIterations

7.4TheHessenbergandRealSchurForms

7.5ThePracticalQRAlgorithm

7.6InvariantSubspaceComputations

7.7TheQZMethodforAx=ABx

8TheSymmetricEigenvalueProblem

8.1PropertiesandDecompositions

8.2PowerIterations

8.3TheSymmetricQRAlgorithm

8.4JacobiMethods

8.5TridiagonalMethods

8.6ComputingtheSVD

8.7SomeGeneralizedEigenvalueProblems

9LanczosMethods

9.1DerivationandConvergenceProperties

9.2PracticalLanczosProcedures

9.3ApplicationstoAx=bandLeastSquares

9.4ArnoldiandUnsymmetricLanczos

10IterativeMethodsforLinearSystems

10.1TheStandardIterations9

10.2TheConjugateGradientMethod

10.3PreconditionedConjugateGradients

10.4OtherKrylovSubspaceMethods

11FunctionsofMatrices

11.1EigenvalueMethods

11.2ApproximationMethods

11.3TheMatrixExponential

12SpecialTopics

12.1ConstrainedLeastSquares

12.2SubsetSelectionUsingtheSVD

12.3TotalLeastSquares

12.4ComputingSubspaceswiththeSVD

12.5UpdatingMatrixFactorizations

12.6Modified/StructuredEignproblems

Index

　　《矩阵计算》一书系统介绍了矩阵计算的基本理论和方法。内容包括矩阵乘法、矩阵分析、线性方程组、正交化和最小二乘法、特征值问题、Lanczos方法、矩阵函数及专题讨论等。本书可作为高等学校数学系高年级本科生和研究生的教材。　　本书系统介绍了矩阵计算的基本理论和方法。内容包括矩阵乘法、矩阵分析、线性方程组、正交化和最小二乘法、特征值问题、Lanczos方法、矩阵函数及专题讨论等。书中的许多算法都有现成的软件包实现，每节后还附有习题，并有注释和大量参考文献。　　本书可作为高等学校数学系高年级本科生和研究生的教材，亦可作为计算数学和工程技术人员的参考用书。