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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£®3£®1 Inverse of a Matrix
1£®3£®2 Matrices and Linear Mappings
1£®3£®3 Operations with Block-Partitioned Matrices
1£®4 Trace and Determinant of a Matrix
1£®5 Rank and Kernel of a Matrix
1£®6 Special Matrices
1£®6£®1 Block Diagonal Matrices
1£®6£®2 Trapezoidaland Triangular Matrices
1£®6£®3 Banded Matrices
1£®7 Eigenvalues and Eigenvectors
1£®8 Similarity Transformations
1£®9 The Singular Value Decompositio£¨SVD£©
1£®10 Scalar Product and Norms iVector Spaces
1£®11 Matrix Norms
1£®11£®1 RelatiobetweeNorms and the Spectral Radius of a Matrix
1£®11£®2 Sequences and Series of Matrices
1£®12 Positive Definite£¬Diagonally Dominant and M-matrices
1£®13 Exercises
2£®Principles of Numerical Mathematics
2£®1 Well-posedness and ConditioNumber of a Problem
2£®2 Stability of Numerical Methods
2£®2£®1 Relations betweeStability and Convergence
2£®3 A priori and a posteriori Analysis
2£®4 Sources of Error iComputational Models
2£®5 Machine Representatioof Numbers
2£®5£®1 The Positional System
2£®5£®2 The Floating-point Number System
2£®5£®3 Distributioof Floating-point Numbers
2£®5£®4 IEClIEEE Arithmetic
2£®5£®5 Rounding of a Real Number iits Machine Repre sentation
2£®5£®6 Machine Floating-point Operations
2£®6 Exercises

II£®Numerical Linear Algebra
3£®Direct Methods for the Solutioof Linear Systems
3£®1 Stability Analysis of Linear Systems
3£®1£®1 The ConditioNumber of a Matrix
3£®1£®2 Forward a priori Analysis
3£®1£®3 Backward a priori Analysis
3£®1£®4 A posteriori Analysis
3£®2 Solutioof Triangular Systems
3£®2£®1 Implementatioof SubstitutioMethods
3£®2£®2 Rounding Error Analysis
3£®2£®3 Inverse of a Triangular Matrix
3£®3 The GaussiaEliminatioMethod £¨GEM£© and LU Factorization
3£®3£®1 GEM as a FactorizatioMethod
3£®3£®2 The Effect of Rounding Errors
3£®3£®3 Implementatioof LU Factorization
3£®3£®4 Compact Forms of Factorization
3£®4 Other Types of Factorization
3£®4£®1 LDMT Factorization
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III£®Around Functions and Functionals
IV£®Transforms£¬Differentiatioand Problem Dis-cretication
References
Index of MATLAB Programs
Index