Topics for the First Midterm

The first midterm exam will concentrate on concepts. For each of the items below you should be prepared to explain the concept. In the case of theorems and definitions, you should be prepared to write out a statement of the theorem or definition. For methods you should be prepared to give an outline of the method.

• Fixed point theorem
• Newton's method for root finding
• Linear convergence
• Quadratic convergence
• Gauss elimination
• Round-off error
• Partial pivoting and scaled partial pivoting
• LU and LUP factorization
• Vector norm
• Matrix norm
• Eigenvalue and eigenvector
• Jacobi and Gauss-Seidel methods
• Condition numbers
• Iterative refinement
• Method of steepest descent
• Conjugate gradient method