Syllabus

Week-By-Week Syllabus

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AG = First Course in Numerical methods

CV = Introduction to Scientific Computing: A Matrix-Vector Approach Using Matlab

Week

Lecture

Notes

1

 Jan 22 Preview Jan 24 Matrix Manipulations
 Fitting an Ellipse to Data    IntroGui.zip CV Chap1, 5.1-5.3, AV Chap 4 The12Commandments.zip

2

 Jan 27 Matrix Set-Up Jan 29 Sparse Matlab, Benchmarking Jan 31 FFT, Wavelet Transforms
 CV: 5.1, 5.3    ShowLowRank, ShowDCTBasis,ShowCubicInterp Bench1 2 3    ShowSparse1 2 3 4 ShowFFTFactors, BenchFFT, ShowCosBasis ShowHaarFactors ShowHaarBasis, SolveHaar A1 Due Feb 2

3

 Feb 3 Linear Systems & SVD Feb 5 LU Factorization Feb 7 Condition & Floating Point
 CV: 6.1, 6.3, 6.4    AG: 4.4, 5.1-5.5,5.8 ShowOrthog, ShowSVD2, ShowSVDImage ShowVector2Norm, LTriSol, UTriSol, GE, ShowGE LU.zip

4

 Feb 10 Pivoting for Stability Feb 12 Positive Definite Systems Feb 14 Cholesky
 CV: 7.3  AG: 5.5 FP_Facts, FP_Magnify, ShowEffectOfCondtion ShowHessLU  A2 Due Feb 13 ShowBandLU, ShowChol, ShowPosDef

5

 Winter Break Feb 19 Banded Systems, LDL Feb 21 Sparse Direct Methods

 AG: 5.6-5.7   CV: 6.2 ShowSherman, ShowLDLPosDef, ShowLDLSemiDef, ShowLDLIndef SparseFactorizations.zip

AG: 5.6-5.7

6

 Feb 24 Nonlinearity Feb 26 Newton and Bisection Feb 28 1-Dim Optimization

Feb 28 is the Midterm cutoff lecture

 CV: 8.1-8.2 ShowSPDopt  BetterRectangles  MySqrt   ShowMySqrt AG: 3.1-3.5 NewtonFractals, MathBookNewton, Bisection, ShowBisection, GlobalNewton, ShowGlobalNewton NewtonVsSecant, Showfzero, FindConj, MiddleRoot, Choose_f, ShowGolden A3 Due March 1

7

 Mar 3 Iterative Ax=b methods Mar 5 Steepest Descent Mar 7 Conjugate Gradient Methods
 ShowGolden ShowTwoMethods, TheLaplacian, ShowLaplacianChol, ShowPoisson CV 8.3 AG: 9.3

8

 Mar 10 Review Mar 12 In Class Midterm Exam Mar 14 Preconditioners
 A4 Due Mar 10 ShowCholInc, ShowSteepestDescent, ShowPCG

9

 Mar 17 Least Squares Mar 19 QR factorization Mar 21 SVD, Givens QR
 ShowLSFit   ShowQR  ShowSVD ShowLSSolvers   ShowQRvsNE   ShowWeightedLS ShowUnderDetermined   ShowGivensQR CVL 7.1-7.2   AG 61.-6.2

10

 Mar 24 Symmetric Eigenproblem Mar 26 Lanczos Method Mar 28 Jacobi's Method
 RankRevelation   ShowQRP   QRvsSVD   ShowRankDefLS1  ShowRankDefLS2    LSviaQRP    LSviaSVD symSchur2, ShowEig,  JacobiClassical, JacobiCyclic, ShowJacobi A5 Due Mar 28

Spring Break

Week

Lecture

Notes

11

 Apr 7 Tridiagonal Methods Apr 9 Power methods Apr 11 Lanczos Method
 AG: 3.1-3.5 CV: 8.1-8.2 ShowTriDiagEigs, ShowHessOfSym, ShowPowerMethod ShowWielandt, ShowGershgorin, ShowShiftedSolver, ShowEvecCond ShowLanczos, ShowSVDS

12

 Apr 14 Newton for  Systems Apr 16 Quasi-Newton Methods Apr 18 Model Trust Methods
 ShowFinDiffNewton, ShowQuasiNewton, UpdateQR, Show_fsolve AG:9.1  CV: 8.4 A6 Due Apr 16

13

 Apr 21 Nonlinear Least Squares Apr 23 Nonlinear Least Squares Apr 25 Constrained Optimization
 ShowNONLINSQR AG: 9.3  CV: 8.3 A7 Due Apr 27

14

 Apr 28 Special Topics Apr 30 Special Topics May 2 Special Topics
15
 May 5 Review May 7 Review
 A8 Due May 7

FINAL EXAM:  Wed, May 14   9:00 AM   MLT228: Malott Hall 228-Bache Auditorium. Your leaving-for-the-summer travel arrangements must respect this date.