Iterative Methods for Solving Linear Systems - 2000 Yousef Saad

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1、IterativeMethodsforSparseLinearSystemsYousefSaad615124951114821031371Copyrightc2000byYousefSaad.SECONDEDITIONWITHCORRECTIONS.JANUARY3RD,2000.
PREFACExiiiAcknowledgments.............................xivSuggestionsforTeaching.........................

2、xv1BACKGROUNDINLINEARALGEBRA11.1Matrices..................................11.2SquareMatricesandEigenvalues.....................31.3TypesofMatrices.............................41.4VectorInnerProductsandNorms.....................61.5MatrixNorms..................

3、.............81.6Subspaces,Range,andKernel.......................91.7OrthogonalVectorsandSubspaces....................101.8CanonicalFormsofMatrices.......................151.8.1ReductiontotheDiagonalForm.................151.8.2TheJordanCanonicalForm...........

4、.........161.8.3TheSchurCanonicalForm....................171.8.4ApplicationtoPowersofMatrices................191.9NormalandHermitianMatrices......................211.9.1NormalMatrices.........................211.9.2HermitianMatrices........................241.

5、10NonnegativeMatrices,M-Matrices....................261.11Positive-DefiniteMatrices.........................301.12ProjectionOperators............................331.12.1RangeandNullSpaceofaProjector...............331.12.2MatrixRepresentations...................

6、...351.12.3OrthogonalandObliqueProjectors................351.12.4PropertiesofOrthogonalProjectors................371.13BasicConceptsinLinearSystems.....................381.13.1ExistenceofaSolution......................381.13.2PerturbationAnalysis..............

7、.........39ExercisesandNotes...............................412DISCRETIZATIONOFPDES442.1PartialDifferentialEquations.......................442.1.1EllipticOperators.........................452.1.2TheConvectionDiffusionEquation...............47
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8、initeDifferenceMethods.........................472.2.1BasicApproximations.......................482.2.2DifferenceSchemesfortheLaplaceanOperator.........492.2.3FiniteDifferencesfor1