Numerical Analysis: Linear Algebra

CS 383C / CSE 383C / M 383E / SSC 393C

Unique Numbers: 53140(CS) / 66650(CSE) / 56430(Math) / 58560(SSC)

Course Announcement

Fall 2012
TTh 9:30-11am
Room: WRW 113

Instructor: Inderjit Dhillon (send email)
Office: ACE 2.332
Office Hours: Tue 11am-noon, or by appointment

TA: Nagarajan Natarajan (send email)
Office: ACE 5.302
Office Hours: M 2-3:30pm, W 3:30-5pm

Textbook

  • Numerical Linear Algebra by L. N. Trefethen and D. Bau, SIAM, 1997.

    • Pre-requisites

  • Graduate standing; CS 367 or M 368K; and M 340L, M 341; or consent of instructor.
  • The pre-requisites are meant to ensure that students taking this course have a good knowledge of undergraduate linear algebra, computer programming, and some mathematical sophistication (students should have some experience in writing mathematical proofs).

    • Handouts

  • Class Survey

    • Syllabus

  • Fundamentals (Vectors, matrices, norms, singular value decomposition).
  • QR Factorization and Least Squares (Gram-Schmidt orthgonalization, Householder tridiagonalization, least squares).
  • Conditioning and Stability (Condition numbers, floating point arithmetic, analysis of specific algorithms).
  • Solving systems of equations (Gaussian Elimination, pivoting, stability, Cholesky factorization).
  • The Eigenvalue Problem (Reduction to Hessenberg or Tridiagonal form, bisection+inverse iteration, Rayleigh quotient iteration, QR algorithm, SVD computation).
  • Iterative Methods.

    • Grading

  • 30% midterm (1 exam)
  • 40% final exam
  • 25% homeworks
  • 5% class participation and attendance

    • Other Books

  • Fundamentals of Matrix Computations by David Watkins, 3rd Ed., 2010. Very readable textbook.
  • Applied Numerical Linear Algebra by James W. Demmel, SIAM, 1997.
  • Matrix Computations by G. Golub and C. Van Loan, 3rd Ed. Johns Hopkins Press, 1996. Encylopedic reference for matrix computations.

    • Background Material

  • Strang's Video Lectures on Linear Algebra, Undergraduate course, MIT, Fall 1999.

    • Code of Conduct: http://www.cs.utexas.edu/users/ear/CodeOfConduct.html