CAAM 353 Computational Numerical Analysis Spring 2008

general information lectures assignments

Notes are posted in PDF. A free PDF viewer is available for most computer systems from clicking on the the icon shown below.

• Week 1 (1/8, 1/10): Gaussian elimination and LU decomposition.
  • Chapter 2 in Cleve Moler: Numerical Computing with Matlab.
  • Handout:
    linear_systems1.pdf,
    linear_systems2.pdf.
  • Matlab:
    gauss.m, utriangsl.m, testgauss.m
    lu_pp.m, lu_pp_sl.m, testlu_pp.m
    
• Week 2 (1/15, 1/17): Gaussian elimination and LU decomposition. How do we get P, L and U; using the LU decomposition.
  • Chapter 2 in Cleve Moler: Numerical Computing with Matlab.
  • Handout:
    linear_systems2.pdf.
  • Matlab:
    lu_pp.m, lu_pp_sl.m, testlu_pp.m
    
• Week 3 (1/22, 1/24): Solution of systems of linear equations with special structure.
  • Chapter 2 in Cleve Moler: Numerical Computing with Matlab.
  • Handout:
    linear_systems3.pdf.
  • Matlab:
    mychol.m, testchol.m
    truss.pdf truss.m, transmission_tower.m, stiff.m, truss_plot.m
    bvp.m, tridiag_lu.m, tridiag_lu_sl.m
    
• Week 4 (1/29, 1/31): Floating Point Arithmetic
  • Sections 1.7, 2.6, 2.8, 2.9 in Cleve Moler: Numerical Computing with Matlab.
  • Handouts:
    • Floating Point Arithmetic: floating_point.pdf.
  • Matlab:
    demo_fl_1.m, demo_fl_2.m, sfl.m, sflop.m.
  • Additional reading:
    • SUN Microsystems Numerical Computation Guide
    • What every computer scientist should know about floating-point arithmetic by D. Goldberg.
    • Christopher Essex, Matt Davison, and Christian Schulzky. Numerical Monsters, SIGSAM Bull., Vol 34, No. 4, 2000, pages 16-32
    • Some disasters attributable to bad numerical computing, compiled by Douglas Arnold.
    • Collection of software bugs, compiled by Thomas Huckle.
• Week 5 (2/5, 2/7): Error Analysis
  • Sections 1.7, 2.6, 2.8, 2.9 in Cleve Moler: Numerical Computing with Matlab.
  • Handouts: error_analysis.pdf, linear_systems_error_analysis.pdf.
  • Matlab:
    demo_cond.m,
    demo_lu_fl.m, lu_pp_fl.m, lu_pp_sl_fl.m, sfl.m, sflop.m.
• Week 6 (2/11, 2/14): Linear Least Squares
  • Chapter 5 in Cleve Moler: Numerical Computing with Matlab.
  • Handouts: linear_least_squares.pdf
    
  • Matlab:
    Filip.dat, lls_demo.m. For info on the data set see the NIST web-page.
    lls_rank.m,
• Week 7 (2/19, 2/21): Linear Least Squares, Regularized Least Squares
  • Chapter 5 in Cleve Moler: Numerical Computing with Matlab.
  • Handouts: linear_least_squares_reg.pdf
    
  • Matlab:
    Filip.dat, lls_demo.m. For info on the data set see the NIST web-page.
    lls_rank.m,
• Week 8 (2/26, 2/28): Application of Regularized Least Squares: Data Assimilation
  Solution of Nonlinear Equations (Bisection)
  • Chapter 4 in Cleve Moler: Numerical Computing with Matlab.
  • Handouts: linear_least_squares_reg.pdf
    rootfinding1d.pdf.
• Week 9: Spring break
• Week 10 (3/11, 3/13): Solution of Nonlinear Equations
  • Chapter 4 in Cleve Moler: Numerical Computing with Matlab.
  • Handouts: rootfinding1d.pdf, rootfindingnd.pdf
    
  • Matlab: bisect.m, regulafalsi.m, newt1d.m, secant.m, coscosh.m, xsinx2.m, nlineq_driver.m.
    newtnd.m, fdnewtnd.m, shamnd.m, broyden.m.
    driver.m, ex1.m.
    driver_ex2.m, ex2.m.
    driver_chandra.m, chandra.m.
• Week 11 (3/18, 3/20): Complete solution of systems of linear equations. Polynomial Interpolation
  • Chapter 3 in Cleve Moler: Numerical Computing with Matlab.
  • Handouts: polyinterp.pdf
    
  • Matlab: demo_pol_bases.m
    NewtIntPol.m, NewtIntPolEval.m, AitkenNeville.m, testint.m.
    
• Week 12 (3/25, 3/27): Polynomial Interpolation and Splines
  • Chapter 3 in Cleve Moler: Numerical Computing with Matlab.
  • Handouts: polyinterp.pdf, splines.pdf
    
  • Matlab: demo_pol_bases.m
    NewtIntPol.m, NewtIntPolEval.m, AitkenNeville.m, testint.m.
    ccspline.m, cfspline.m, csplineeval.m, demo_spline.m.
    tridiagLDL.m tridiagLDLsl.m.
    
• Week 13 (4/1, 4/3=spring recess): B-Splines and Bezier curves
  • Chapter 3 in Cleve Moler: Numerical Computing with Matlab.
  • Handouts: splines.pdf, bezier_bsplines.pdf
    
  • Matlab: ccspline.m, cfspline.m, csplineeval.m, demo_spline.m.
    tridiagLDL.m tridiagLDLsl.m.
    
• Week 14 (4/8, 4/10): Integration
  • Chapter 6 in Cleve Moler: Numerical Computing with Matlab.
  • Handout: integration.pdf
    
  • Matlab: composite.m
    driver.m, trapcomp.m, simpcomp.m
    romberg.m, simpadpt.m
    
• Week 15 (4/15, 4/17): Solution of Ordinary Differential Equations
  • Chapter 7 in Cleve Moler: Numerical Computing with Matlab.
  • Handouts:
    • Systems of Ordinary Differential Equations (ODEs): Examples and (some) Theory: ode1.pdf.
    • Elementary Methods for the Solution of ODEs: ode2.pdf
    • Runge Kutta Methods for the Solution of ODEs: ode3.pdf
  • Matlab:
    ExpEuler.m, ImpEuler.m, ChemReac.m, Ex1.m, PredPrey.m, PredPrey2.m, ode_drv.m
    ode23tx.m, ChemReac23.m, ode23_drv.m
    
• Week 16 (4/22): Solution of Ordinary Differential Equations

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