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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
����
III��Around Functions and Functionals
IV��Transforms��Differentiatioand Problem Dis-cretication
References
Index of MATLAB Programs
Index
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