Function: franaiter
FRANAITER  Iterative analysis
  Usage:  c=franaiter(F,f);
          [c,relres,iter]=franaiter(F,f,...);

  Input parameters:
        F       : Frame.
        f       : Signal.
        Ls      : Length of signal.
  Output parameters:
        c       : Array of coefficients.    
        relres  : Vector of residuals.
        iter    : Number of iterations done.

  c=FRANAITER(F,f) computes the frame coefficients c of the signal f*
  using an iterative method such that perfect reconstruction can be
  obtained using FRSYN. FRANAITER always works, even when FRANA
  cannot generate perfect reconstruction coefficients.

  [c,relres,iter]=FRANAITER(...) additionally returns the relative
  residuals in a vector relres and the number of iteration steps iter.
 
  *Note:* If it is possible to explicitly calculate the canonical dual
  frame then this is usually a much faster method than invoking
  FRANAITER.

  FRANAITER takes the following parameters at the end of the line of
  input arguments:

    'tol',t      Stop if relative residual error is less than the
                 specified tolerance. Default is 1e-9 (1e-5 for single precision)

    'maxit',n    Do at most n iterations.

    'pg'        Solve the problem using the Conjugate Gradient
                 algorithm. This is the default.

    'pcg'        Solve the problem using the Preconditioned Conjugate Gradient
                 algorithm.

    'print'      Display the progress.

    'quiet'      Don't print anything, this is the default.

  Examples
  --------

  The following example shows how to rectruct a signal without ever
  using the dual frame:

     f=greasy;
     F=frame('dgtreal','gauss',40,60);
     [c,relres,iter]=franaiter(F,f,'tol',1e-14);
     r=frsyn(F,c);
     norm(f-r)/norm(f)
     semilogy(relres);
     title('Conversion rate of the CG algorithm');
     xlabel('No. of iterations');
     ylabel('Relative residual');

Url: http://ltfat.github.io/doc/frames/franaiter.html

See also: frame, frana, frsyn, frsyniter.

Package: ltfat