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
 RandomStoch, ShowPageRank, ShowBlockMarkov, StationaryVec  
 
 
    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.