473 Handouts and Worksheets

• A Practical Introduction to Matlab (Version 5) (html version) (by Mark Gockenbach) or Postscript version
• For more introductory material and tutorials see the main course page
• Additional reading
• Introductory Matlab scripts
  • basic_definitions.m (script that calls all other files. Note, however, that each file below can also be executed separately.)
  • matrix_vector.m (definition of matrices and vectors)
  • arithmetic.m (simple arithmetic with matrices and vectors)
  • lin_sys.m (solving linear systems)
  • submatrices.m (definition of submatrices)
  • statistics.m (timing in Matlab)
  • loops.m (for-loops, and why to avoid them)
  • plotting.m (simple plotting)
  • user_defined_functions.m (how to use user-defined functions)
  • circle.m (a user-defined function)
  • basics.zip (.zip file containing all of the files above)
• Matlab scripts for simple image compression
  • lu_compression.m (image compression based on partial LU decomposition)
  • qr_compression.m (image compression based on partial QR decomposition)
  • svd_compression.m (image compression based on partial singular value decomposition)
  • compression.zip (.zip file containing all of the files above)
• GramSchmidt.m (Example 2 in Trefethen/Bau, Sect.9. Requires two additional m-files clgs.m and mgs.m to be supplied by the user)
• Matlab scripts for polynomial least squares fitting
  • PolynomialLSQ.m (Matlab function that computes and plots polynomial interpolant / least-squares fit)
  • PolynomialDemo.m (Matlab script that calls PolynomialLSQ.m)
  • Polynomial.zip (.zip file containing the two files above)
• 473_stability.mws (Maple worksheet that illustrates stable and unstable algorithms)
• Matlab scripts to illustrate stability of least squares algorithms
  • LSQ_Stability_book.m (Matlab script that does stability examples from Trefethen/Bau Sect.19)
  • LSQ_Stability.m (same as above with different function to be fitted)
  • LSQ_Stability.zip (.zip file containing the two files above)
• 473_LU.mws (Maple worksheet that motivates LU factorization and partial pivoting)
• 473_Hessenberg.mws (Maple worksheet that illustrates use of Householder reflections for reduction to upper Hessenberg form)
• RayleighQuotient.m (Matlab script) to compare convergence of inverse iteration and Rayleigh quotient iteration)
• 473_IterativeSolvers.mws (Maple worksheet that illustrates classical iterative linear system solvers)
• GMRESDemo.m (Matlab script that demonstrates convergence of the GMRES method)
• Matlab scripts to illustrate the conjugate gradient algorithm
  • CGDemo.m (Matlab script that demonstrates convergence of the conjugate gradient method)
  • PCGDemo.m (Matlab script that compares conjugate gradient method with and without preconditioning)
  • CGDemos.zip (.zip file containing the two files above)