References to the items that are discussed in PressRef.htm are footnoted.
The subjects covered are:
A.functions as arguments, command line input
B. static_variables, calloc Fort calls C
II. The AMOEBA[1] -- for people with more computer time than experience
Finding the error in an amoeba minimum Errinfun
III. Lagrange interpolation[2]
A. Selection of the “best” set of N unevenly spaced points -- Findfun
B Filon's method for calculating
a Fourier transform. Fourier1.doc - Filon_transform
IV. Integration Partition
A. Trapezoidal rule integration\CINT1.doc including Romberg extrapolation[3].
B. Gauss Quadrature[4] -- Orthogonal Polynomials CINT2.DOC Cint3.doc Cint4.doc
Multidimensional integration assignment Assign.doc
C. Monte-Carlo (biased selection) Guiding function in mcarlo, details in MonteCarlo
V. Fourier Transform methods Fourier1
A. Convolution[5] Convolution
B. Solution of a differential equation in transform space. -- Green's function diffFT
C. The Fast Fourier Transform[6] Fourier2
VI. Differential equations[7] DIFFEQ1
A. Euler’s method[8] DIFFEQ1- Euler
B. Runge-Kutta[9] DIFFEQ1 - RungeKutta
D. Predictor Corrector with mid-point[10] DIFFEQ1 - predcorr
C. Boundary value problems (finding eigenvalues and eigenfunctions)[11] shoot.doc
D. Newton's method Newton.doc and Aitkin's extrapolation Aitkins.doc
E. Relaxation methods Jacobi.doc jacobi2.DOC
VII. Optimization
A. Gauss-Jordan[12] GaussJ.doc, and Cholesky matrix inversion.Cfposdef - cholesky
B. Modified Newton Raphson[13] --Robmin details more experience than computer time
A few programming and matrix techniques will be needed to get through this list. A large fraction of physics reduces to the problem of evaluating an integral to find the action as a function of a set of constants and then minimizing the action with respect to these constants. This course should show you how to tackle this problem.
[1] Press (1986 Fortran) p292 -- I do not agree with all of his default settings.
[2] Ibid. p. 80 --- He scoff's at my notion that this is a best method
[3] Ibid. p9 102-103 --- I do not trust his method of estimating errors
[4] Ibid. pp. 121-126 --- Gives codes for generating weights, I suspect that many will prefer to look them up.
[5] Ibid. pp. 407-414 --- Cannot imagine a convolution without the FFT and thus discusses it after the FFT
[6] Ibid. pages 381-386 Give Press's definition of Fourier transforms -- half the world uses the opposite sign conventions 3/4 do not use the 2 p -- I agree with Press.
386-390 -- brief explanation of the FFT algorithm.
[7] Ibid. pp. 547 -577
[8] Ibid. p 550
[9] Ibid. pp 550-560
[10] Ibid. pp. 561-562 Press does not like predictor corrector nor understand this simple method. His statement about only even powers is false. His discussion of Stiff Sets of equations pp. 572-577 is very relevant.
[11] Ibid. pp. 578-600 Beware of Press, "We always shoot first, and only then relax." P 581
[12] Ibid. pp. 24-29
[13] Ibid. pp. 523-528 I have extended the Marquardt method considerably -- come to class.