Numerical Linear Algebra

Numerical Linear Algebra

1. Vectors, matrices, norms.

2. Orthogonal factorizations:
      Singular Value Decomposition
      QR factorization
      Gram-Schmidt orthogonalization
      Householder reflectors

2. Least squares problems:
      Orthogonal projections
      Moore-Penroose pseudoinverse

3. Machine arithmetics, floating point representation

4. Stability and conditioning of problems

5. Gaussian elimination

6. Eigenvalue problems
      Reduction to Hessenberg form
      Power, inverse power and Rayleigh quotient iterations
      Simultaneous iterations and QR algorithm