## 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