Fall 2018 - Scientific Computing I

Updated 11/20/2018.

Syllabus

Final Exam Main references
  • Principles of scientific computing, Bindel, Goodman here.
  • Numerical optimization, Nocedal, Wright here.
  • Afternotes in Numerical Analysis, Stewart here.
  • Lecture notes on ODEs, Strain here.
Additional material
  • Numerical Computing with IEEE Floating Point Arithmetic by M. Overton Available online here
  • Numerical analysis by T. Sauer,
  • David Bindel's class page
  • 08/28 Sources of error Chpt 2 from Bindel, Goodman here,
  • 08/30 Sources of error Chpt 2 from Bindel, Goodman.
  • HW1
  • 09/04 Linear Algebra I Chpt 4 from Bindel, Goodman.
  • Vector spaces, Matrices and linear transformations.
  • HW2
  • 09/06 Linear Algebra I Chpt 4 from Bindel, Goodman.
  • Adjoint operators, vector and matrix norms,eigenvalue problem.
  • 09/11 Linear Algebra I Chpt 4 from Bindel, Goodman.
  • Eigenvalue problem, Differentiation and perturbation theory, variational principles.
  • 09/13 Lecture moved to 09/11 Software and coding principles.
  • Discussion of a Plane Wave problem to illustrate.
  • 09/18 Linear Algebra I Chpt 4 from Bindel, Goodman.
  • Variational principles for symmetric eigenvalue problems, least squares, singular values and principal components.
  • HW3
  • 09/20 Linear Algebra I Chpt 4 from Bindel, Goodman.
  • Singular value decomposition, condition number.
  • 09/25 Linear Algebra II Chpt 5 from Bindel, Goodman.
  • Gauss elimination, LU decomposition.
  • HW4
  • 09/27 Linear Algebra II Chpt 5 from Bindel, Goodman.
  • Choleski factorization, Least squares and QR factorization.
  • 10/02 Nonlinear equations Chpt 11 from Nocedal, Wright.
  • Comments on software. Newton's method.
  • 2nd UPDATED HW5
  • 10/04 Nonlinear equations Chpt 11 from Nocedal, Wright.
  • Inexact Newton methods and Broyden's method.
  • 10/09 Nonlinear equations Chpt 11 from Nocedal, Wright.
  • Tensor methods, a hybrid method (From Lecture 5 in the Afternotes). Merit functions, line search methods.
  • HW6, see Bisection function, Hybrid method function.
  • 10/11 Nonlinear equations Chpt 11 from Nocedal, Wright.
  • Trust regions, Continuation/homotopy methods.
  • 10/16 Fundamentals of unconstrained optimization Chpt 2 from Nocedal, Wright.
  • HW7
  • 10/18 Line search methods Chpt 3 from Nocedal, Wright.
  • 10/23 Line search methods Chpt 3 from Nocedal, Wright.
  • HW8
  • 10/25 Trust-region methods Chpt 4 from Nocedal, Wright.
  • 10/30 Trust-region methods Chpt 4 from Nocedal, Wright.
  • HW9 and codes.
  • 11/01 Conjugate Gradient methods Chpt 5 from Nocedal, Wright.
  • Conjugate direction method. Basic properties of the CG method.
  • 11/06 Conjugate Gradient methods Chpt 5 from Nocedal, Wright.
  • Practical CG method. Rate of convergence. Preconditioning.
  • No HW
  • 11/08 Odrinary Differential Equations
  • 11/13 Odrinary Differential Equations
  • 11/15 Odrinary Differential Equations
  • 11/20 Conjugate Gradient methods Chpt 5 from Nocedal, Wright.
  • Practical precontinioners. Nonlinear CG methods.
  • HW10

Teaching at UMD

Teaching at NYU

Teaching activities at UPMC - Paris 6

  • LM201 Analysis and algebra (2nd year) (Fall 2010, Fall 2011, Fall 2012).
  • LM334 TA for Introduction to numerical analysis (3rd year) (Fall 2012).
  • LM350 TA for Topology and diff. calc. (3rd year) (Fall 2010, Fall 2011).