instructor: Julien Langou

course title: Numerical Linear Algebra

description: Numerical Linear Algebra is at the foundation of many scientific computation. This course introduces the techniques, analysis methods, and implementation details of numerical linear algebra. The course emphasizes the link between theoretical concepts, algorithm formulation, and practical implementation. The class will cover the main matrix algorithms for LU, QR, Cholesky, LDLT, linear least squares, Schur form, diagonalization, symmetric and nonsymmetric eigenvalue problems, and singular value decomposition. During this journey, we will study (1) the theory of error analysis, condition number, forward and backward error, (2) how to write implementations in term of matrix-matrix multiplication so as to get efficiency, (3) the amount of memory transfer between different level of memory during a computation, (4) parallel implementations of these algorithms using MPI or task-based programming, (5) an introduction to randomized linear algebra techniques.

evaluation The class will have (1) quizes to assess students learning of the theory, and (2) programming assignments to assess students learning of the practice.

bibliography The course will rely on research articles in the area. For some relevant textbook that will give some background, see:

  • Numerical Linear Algebra, by Lloyd N. Trefethen and David Bau, III, SIAM, 1997
  • Numerical Linear Algebra with Julia, by Eric Darve and Mary Wootters, SIAM, 2021
  • Matrix Computations, fourth edition, by Gene H. Golub and Charles F. Van Loan, Johns Hopkins University Press, 2013
  • Applied Numerical Linear Algebra, by James W. Demmel, SIAM, 1997