Course information

Semester 2

Time and Place
Sunday
14:00-15:45
Sprintzak 24 (exer.)
וקדגשטד
12:00-13:45
Sprintzak 114 (class)

 

Teacher: Raanan Fattal

Syllabus (tentative)

  Topic Description
  Interpolation Polynomial, Spline, Least-Squares, Regular Grid, Scattered Data Interpolations. Error of Polynomial Interpolation.
  Integration Newton-Cotes, Integration Error, Monte Carlo Integration and Rejection Sampling.
  Nonlinear Systems Bisection, Secant, and Newton Methods.
  Linear Systems LU and Cholesky decomp., Iterative Solvers, Conjugate Gradients, Preconditioning, QR.
  Eigendecompositions (Inv.) Power Method, Jacobi Iteration, Hessenberg Form.
  Optimization Analytical Optimization and Simulated Annealing.
  Ordinary Differential Eqns. Euler method, Runge-Kutta, Midpoint and Single Step Methods.
 
 

References

  • Numerical Recipes: The Art of Scientific Computing by William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery [pdf]
  • Numerical Analysis: Mathematics of Scientific Computing by David R. Kincaid and E. Ward Cheney
  • Analysis of Numerical Methods by Eugene Isaacson
  • Introduction to Conjugate Gradient, Jonathan Shewchuk, [pdf]
  • Iterative methods for sparse linear systems, Yousef Saad, [pdf]
  • Numerical Methods for Large Eigenvalue Problems, Yousef Saad [pdf]
  • Introduction to Numerical Analysis: Second Edition, Dover Books, by F. B. Hildebrand

Course notes by Dina Zeliger and exam notes

MATLAB Tutorials: here, here, and here, example file here

Course Assignments

Topic
File
Date due
Lin. Alg & Calc.

Interpolation

Integration

Systems

Eig. dec. + ODEs