Notes for MA580 (old MA529):
This notes consist mainly of those topics in numerical linear algebra.
The chapters are organized as as follows:
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
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Singular Value Decomposition
Chapter 5, Algebraic
Eigenvalue Problems (postscript)
(pdf)
-
Location and Perturbation Results
-
Power Methods and Inverse Power
Methods
-
QR Algorithm