Scientific computing - selected example solutions to midterm problems

span style="color: #228B22;">% solves QMQ^-1 v = l*v for lambda - dominating eigenvalue
 
% it is equivalent to MQ^-1v = l*Q^-1 v or My = l * y with v = Q*y
% if, of course, Q is nonsingular; 
% note that usually Q will be singular so our reformulation makes the problem well posed even for singular Q
% check if Q is singular... (if someone insists, because this takes both time and memory!)
% extract diagonal only
% note that computing the norm of an eigenvector is a NONSENSE!

span style="color: #228B22;">% these are squares of dist
% compute omega at rectangular gridpoints (x,y) (e.g. returned by meshgrid)
% for FD approx only
% exact formula: takes effort to derive
% quick and dirty approximation
% for FD approx only
% plot 
% restiricting to 1-D problem:
%g can be inaccurate: fsolve exit code: %d\n', x(1), info));