Notes for MA580:

These notes cover mainly those topics in numerical linear algebra. The lectures are organized as follows. Additional materials, including those graphical demonstrations and some newly developed techniques, will be added in class.

Chapter 1,    Error Analysis (postscript) (pdf)

•         Measurement of Errors
•         Representation of Numbers
•         Stability and Conditioning

Chapter 2,    System of Linear Equations - Direct Approach (postscript) (pdf)

•         General Consideration
•         Gaussian Elimination
•         Mathematical Pivoting
•         Error Analysis
•         Orthogonal Decomposition

Chapter 3,    System of Linear Equations - Iterative Approach (postscript) (pdf)

•         General Consideration
•         Relaxation Methods
•         Acceleration Methods
•         Conjugate Gradient Methods

Chapter 4,    Least Squares Problems (postscript) (pdf)

•         Linear Least Squares Problems
•         Singular Value Decomposition

Chapter 5,    Algebraic Eigenvalue Problems (postscript) (pdf)

•         Location and Perturbation Results
•         Power Methods and Inverse Power Methods
•         QR Algorithm