Math 441, Introduction to Numerical Analysis
Fall 2006
Preparation for Test 2
Our second test on Thursday, November 2. The test will be on the material
studied in class since our first test, up to and including the lecture on Thursday, October 26.
No calculators or textbooks allowed.
Material:
- Netwon's method. Contractive mappings. The contraction principle. Attracting and repelling fixed points. (covered in
Lectures 9 and 10, refer to lectures outlines)
- Normed vector spaces. Matrix (subordinate) norms and spectral radius. Condition number of a matrix. (Lectures 8 and 13)
- Iterative methods for linear systems: the basic (Richardson iteration), Jacobi iteration, Gauss-Seidel iteration.
Relationship between condition number and convergence of the damped Jacobi iteration for SPD systems. (lectures 11, 12, 13)
- Main theorem about the conjugate algorithm. (lectures 14, 15)
- Interpolation of functions. Newton and Lagrange forms of the interpolation polynomial. (Lecture 16)
Suggestions for studying:
- Read the solved problems in the textbook. Study the homework problems
and the provided solutions.
- Know the definitions and understand the basics well.
- Know the statements of the basic theorems.