MATH 3241 / COSC 3121 Numerical Methods I:
Test2 Topics
For test 2,
in addition to the topics for test 1 (see Test 1 Topics),
you should be familiar with most of the material in the
following sections of "Numerical Analysis"
(7th ed.)
by Burden and Faires
Section 6.1 Linear Systems of Equations
Section 6.2 Pivoting Strategies
Section 6.3 Linear Algebra and Matrix Inversion
Section 6.4 The Determinant of a Matrix
Section 6.5 Matrix Factorization
Section 6.6 Special Types of Matrices
Section 7.1 Norms of Vectors and Matrices
(Note: There will be no question of
proving vector and matrix norms on Test 2.
)
Section 7.2 Eigenvalues and Eigenvectors
Section 7.3 Iterative Techniques for Solving Linear Systems
Section 7.4 Error Bounds and Iterative Refinement
Here are some topics you should be familiar with (and in addition to the topics for test 1 (see Test 1 Topics)):
- Gaussian Elimination
- Backward Substitution
- Partial Pivoting
- Scaled Partial Pivoting
- Algorithm and Counting Operations
- Triangular Matrices, Tri-diagonal Matrices and diagonal Matrices
- Evaluating Inverses
- Evaluating Determinants
- LU Factorization
- Forward Substitution
- Special Matrices(Positive Definite, Strictly
Diagonally Dominant)
- LDL^t and LL^t(Choleski's) Factorizations
- Crout's Factorization for Tri-diagonal linear systems
- Norms of Vectors and Matrices
( Note: There will be no question of
proving vector and matrix norms on Test 2.
)
- Eigenvalues, and Spectral Radius
- Convergent Matrix
- Jacobi Iterative Method
- Gauss-Seidel Iterative Method
- SOR Method
- Condition Number
- Iterative Refinement