UW AMath

AMath 584, Autumn Quarter, 2011

Applied Linear Algebra and

Introductory Numerical Analysis

Table Of Contents


We will cover much of parts I through V of Trefethen and Bau, along with some supplementary material.

Some major topics

  • Review of basic linear algebra in finite dimensional spaces, including both R^n and also function spaces.
  • Linear independence, bases, norms, matrix factorization, etc.
  • Orthogonality and the Singular Value Decomposition (SVD).
  • Least squares problems: QR factorizations, Gram-Schmidt, Householder transformations.
  • Conditioning of problems and stability of algorithms.
  • Linear systems of equations: Gaussian elimination and LU factorizations.
  • The eigenvalue problem: the power method and QR algorithms, relation to SVD.
  • Various applications of the above algorithms will also be considered.