CAAM 454: Project

Due 4/23, Wed., 8:00pm on OwlSpace

Guidelines

• Please see the PDF file proj_invp.pdf for a description of the project.
• Implement two methods: gradient method and Gauss Newton.
• Write a Matlab function as specified below:

  function [x,iter,nf,fh,gh] = mysolver(func,x0,tol,maxit,method,varargin)
  %
  % Solver for least squares problems min f(x) = 0.5*r(x)'*r(x)
  %
  % Output:
  %   x -- solution
  %   iter -- number of iterations taken
  %   nf -- number of func evaluations
  %   fh -- function values at all iterations
  %   gh -- gradient norms at all iterations
  % Input:
  %   func -- function (handle) that returns [r, J] for given x
  %   x0 -- initial guess for x
  %   tol -- tolerance for gradient norm
  %   maxit -- maximum allowable iteration number
  %   method -- 1 for gradieng, 2 for Gauss-Newton
  

  And implement a function to compute [r, J] for the inverse problem where the 2 unknown parameters are the constant and the slope (in that order for s_1 and s_2) of a linear function.
• Download the instructor's codes zsolver.p, zinvprJ.p, zgetAb.p and the test script testinvp.m.
• To test the correctness and versatility of your code, run the test script for different parameter values, say

           E =   1  10  10  5  10  2  1  5
           k =   2   3   5  1   5  2  2  1
      method =   1   1   1  1   2  2  2  2
  

  Report your results in comparison with the instructor's code.
• To test the efficiency of your code, run the test script for some large values (say, n=5000 or larger, E=50 or larger and k=5) for both methods. Report your results in comparison with the instructor's code. Submit output of the testscript for such "large runs", and the output from running the script hist_plot.m; along with your codes and report.
• Try to report your insights into the problem and algorithms, based on your experiments and observations. Observations without insights are less meaningful.

Rules

• Discussions with the instructor are encouraged, but otherwise the project must be done independently. You report must be "pledged".