Numerical Linear Algebra and Its Applications

Preface
Chapter 1 Introduction
1．1 Basic symbols
1．2 Basic problems in NLA
1．3 Why shall we study numerical methods?
1．4 Matrix factorizations (decompositions)
1．5 Perturbation and error analysis
1．6 Operation cost and convergence rate
Exercises

Chapter 2 Direct Methods for Linear Systems
2．1 Triangular linear systems and LU factorization
2．2 LU factorization with pivoting
2．3 Cholesky factorization
Exercises

Chapter 3 Perturbation and Error Analysis
3．1 Vector and matrix norms
3．2 Perturbation analysis for linear systems
3．3 Error analysis on floating point arithmetic
3．4 Error analysis on partial pivoting
Exercises

Chapter 4 Least Squares Problems
4．1 Least squares problems
4．2 Orthogonal transformations
4．3 QR decomposition
Exercises

Chapter 5 Classical Iterative Methods
5．1 Jacobi and Gauss-Seidel method
5．2 Convergence analysis
5．3 Convergence rate
5．4 SOR method
Exercises

Chapter 6 Krylov Subspace Methods
6．1 Steepest descent method
6．2 Conjugate gradient method
6．3 Practical CG method and convergence analysis
6．4 Preconditioning
6．5 GMRES method
Exercises

Chapter 7 Nonsymmetric Eigenvalue Problems
7．1 Basic properties
7．2 Power method
7．3 Inverse power method
7．4 QR method
7．5 Real version of QR algorithm
Exercises

Chapter 8 Symmetric Eigenvalue Problems
8．1 Basic spectral properties
8．2 Symmetric QR method
8．3 Jacobi method
8．4 Bisection method
8．5 Divide-and-conquer method
Exercises

Chapter 9 Applications
Bibliography
Index