### 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