Numerical Analysis: Numerical Linear Algebra


ACM 110, Fall Quarter 2001
Mondays, Wednesdays, Thursdays, 3:00-4:00 p.m. in Firestone 308

Instructor: Hao-Min Zhou (email: hmzhou@acm.caltech.edu)
Office Hours: Mon., Wed. 2:00-3:00 p.m. or by appointment
TA: Xinwei Yu (email: xinwei@its.caltech.edu)


Course Information


Reference Books:

  • Numerical Linear Algebra, by Lloyd N. Trefethen and David Bau
  • Iterative Methods for Sparse Linear Systems, by Yousef Saad
  • Matrix Computations, by Gene Golub and Charles Van Loan
  • Iterative Solution of Large Sparse Linear Systems of Equations, by W. Hackbusch


    • Course Materials:

  • Fundamentals of Linear Algebra: Norms, SVD.
  • Direct Methods: LU Factorization, Stability, Pivoting, Cholesky Factorization.
  • Eigenvalue Problems: Hessenberg, Schur decomposition, Rayleigh Quotient, Inverse methods, QR Factorization, Gram-Schmidt Orthogonalization, Householder, Givens Triangularization, QR methods, SVD Computing.
  • Iterative Methods: Classical iterations, Krylov subspace methods, Arnoldi iteration, GMRES, Lanczos, Conjugate Gradient(CG), preconditioning.
  • Advanced Topics: introduction to multigrid and domain decomposition methods.

    • Grading:

    75% of your final grade is based on your homework (5 sets, 15% for each set) and 25% is on the final project. In general, late homework is not accepted. Collaboration is encouraged.


    you can download the Final project (revised version with more hints).