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| Preface I.Getting Started 1.Foundations of Matrix Analysis 1.1 Vector Spaces 1.2 Matrices 1.3 Operations with Matrices 1.4 Trace and Determinant of a Matrix 1.5 Rank and Kernel of a Matrix 1.6 Special Matrices 1.7 Eigenvalues and Eigenvectors 1.8 Similarity Transformations 1.9 The Singular Value Decomposition（SVD） 1.10 Scalar Product and Norms in Vector Spaces 1.11 Matrix Norms 1.12 Positive Definite，Diagonally Dominant and M-trices 1.13 Exercises 2.Principles of Numerical Mathematics II.Numerical Linear Algebra 3.Direct Methods for the Solution of Linear Systems 4.Iterative Methods for Solving Linear Systems 5.Approximation of Eigenvalues and Eigenvectors III.Around Functions and Functionals 6.Rootfinding for Nonlinear Equations 7.Nonlinear Systems and Numerical Optimization 8.Polynomial Interpolation 9.Numerical Integration IV.Transforms,Differentiation and Problem Dis-cretication 11.Numerical Solution of Ordinary Differential Equations 12.Two-Point Boundary Value Problems 13.Parabolic and Hyperbolic Initial Boundary Value Prob-lems References Index of MATLAB Programs Index |
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