Numerical Analysis

PrefaceList of Commonly Used SymbolsIntroduction Chapter 1 Linear Algebra 1.1 Eigenvalues and Canonical Forms 1.2 Vector Norms 1.3 Matrix NormsPart I Mathematically and Ill Conditioning Chapter 2 Systems of Linear Algebraic Equations 2.1 Basic Error Estimates and Condition Numbers 2.2 A Posteriori Bounds and Eigenvector Computations Chapter 3 Eigenvalues and Eigenvectors 3.1 Continuity Results 3.2 The Gerschgorin and Bauer-Fike Theorems 3.3 Special Results for Symmetric Matrices Chapter 4 Differential and Difference Equations 4.1 Differential Equations 4.2 Difference EquationsPart II Discretization Error Chapter 5 Discretization Error for Initial Value Problems 5.1 Consistency and Stability 5.2 Convergence and Order Chapter 6 Discretization Error for Boundary Value Problems 6.1 The Maximum Principle 6.2 Matrix MethodsPart III Convergence of Iterative Methods Chapter 7 Systems of Linear Equations 7.1 Convergence 7.2 Rate of Convergence 7.3 Applications to Differential Equations Chapter 8 Systems of Nonlinear Equations 8.1 Local Convergence and Rate of Convergence 8.2 Error Estimates 8.3 Global ConvergencePart IV Rounding Error Chapter 9 Rounding Error for Gaussian Elimination 9.1 Review of the Method 9.2 Rounding Error and Interchange Strategies 9.3 Backward Error Analysis 9.4 Iterative RefinementBibliographyIndex