iterative methods for sparse linear systems (saad)

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1、IterativeMethodsforSparseLinearSystemsSecondEdition0.19E+070.10E-06YousefSaadCopyrightc2003bytheSocietyforIndustrialandAppliedMathematicsContentsPrefacexiiiPrefacetosecondedition..................................xiiiPrefacetofirstedition..................................xix1Bac

2、kgroundinLinearAlgebra11.1Matrices.............................11.2SquareMatricesandEigenvalues................31.3TypesofMatrices........................41.4VectorInnerProductsandNorms................61.5MatrixNorms..........................81.6Subspaces,Range,andKernel......

3、............101.7OrthogonalVectorsandSubspaces...............111.8CanonicalFormsofMatrices..................151.8.1ReductiontotheDiagonalForm..........161.8.2TheJordanCanonicalForm............171.8.3TheSchurCanonicalForm............171.8.4ApplicationtoPowersofMatrices........2

4、01.9NormalandHermitianMatrices.................211.9.1NormalMatrices..................211.9.2HermitianMatrices................251.10NonnegativeMatrices,M-Matrices...............271.11Positive-DefiniteMatrices....................321.12ProjectionOperators.......................34

5、1.12.1RangeandNullSpaceofaProjector.......341.12.2MatrixRepresentations..............361.12.3OrthogonalandObliqueProjectors........371.12.4PropertiesofOrthogonalProjectors........381.13BasicConceptsinLinearSystems................391.13.1ExistenceofaSolution..............401.13

6、.2PerturbationAnalysis...............412DiscretizationofPDEs472.1PartialDifferentialEquations..................472.1.1EllipticOperators.................47vviCONTENTS2.1.2TheConvectionDiffusionEquation........502.2FiniteDifferenceMethods....................502.2.1BasicApproxima

7、tions...............502.2.2DifferenceSchemesfortheLaplaceanOperator.522.2.3FiniteDifferencesfor1-DProblems........532.2.4UpwindSchemes.................542.2.5FiniteDifferencesfor2-DProblems........562.2.6FastPoissonSolvers................582.3TheFiniteElementMethod............

8、.......622.4MeshGenerationandRefinement................692.5Fi