BBTools

bbregsolve

This function is not yet fully documented. This is a transcript of the text-formatted help.

bbregsolve  Compute a regularized solution for A*X=B.
   X=bbregsolve(S,T,...), where S is returned by bbpresolve, approximates
   a regularized solution using the filter-factors specified by T:

     'none'     - No regularization
     'Tikhonov' - Tikhonov-regularization
     'Ridge'    - Alias for 'Tikhonov'
     'dsvd'     - Damped svd
     'tsvd'     - Truncated svd
     <interp>   - Arbitrary filter-factors by interpolation

   Except for 'none', the standard regularization methods must be followed
   by a regularization parameter framed in terms of a singular value. In
   particular, the parameter given to 'tsvd' is a threshold for the
   singular value, not the number of singular triplets (of which
   bbregsolve have no knowledge).

   Normally, bbregsolve computes a hybrid solution, which is colored by
   the intrinsic filter-factors of the iterative routine. If T is
   prepended with '!', then bbregsolve will only use vectors that
   converged to the desired tolerance.

   Example: bbregsolve(S,'!tsvd',1e-2) computes a solution that
   approximates the truncated svd using only singular vectors with
   singular values of 1e-2 or higher. It only use triplets that
   converged to the specified tolerance.

   In principle a non-hybrid solution should be closer to the ideal
   solution. However, the method should only be applied when the
   singular space containing the solution have converged, and this
   often requires an impractically large number of iterations.

   A practical way to check this is to compute the regularized solution
   of type '!none'. If the residual is indistinguishable from noise, then
   a non-hybrid solution may be appropiate.

   Custom filter-factors may be specified by an interpolation-scheme
   compatible with interp1, a vector of singular values, and a vector
   with corresponding filter-factors. The interpolation will happen after
   taking the logarithm of the singular values.

   Example: sig=exp(-5:.1:0); xh=bbregsolve(S,'spline',sig,tanh(sig/.15));

   See also bbpresolve, , bblcurve.

bbredimbbrepmat