The presented approach is suitable for dense problems and also applicable where factorization of a problem matrix is available and we are interested in the solution after adding new data to the original problem.

In the future, it will be of interest to study the updating techniques for sparse data problems and for those where the linear least squares problem is fixed and the constraint system is changing frequently.

Allows positive "damping".) lusol Z: MATLAB software for computing a nullspace operator $$Z$$ of the transpose of a sparse matrix $$S$$ (so that $$S^T Z = 0$$) using sparse QR factors of either $$S$$ or $$S^T$$ computed by Suite Sparse QR, or sparse LU factors of either $$S$$ or $$S^T$$ computed by LUSOL.

MATLAB routines and are provided to factorize $$S$$ or $$S^T$$ and to compute products of the form $$w = Zv$$ and $$s = Z^T t$$ for given vectors $$v$$ and $$t$$.

An adaptive weighted least-squares procedure matching nonparametric estimates of the stable tail dependence function with the corresponding values of a parametrically specified proposal yields a novel minimum-distance estimator.

Likelihood-based procedures are a common way to estimate tail dependence parameters.

They are not applicable, however, in non-differentiable models such as those arising from recent max-linear structural equation models.

\end\begin \Vert E-\tilde \tilde \Vert _&= \bigl\Vert (E-Q\tilde) \bigl((Q-\tilde)\tilde\bigr) \bigr\Vert _ \ &\leq\sqrt(\tilde_ \tilde_ \tilde_)\max \left(, \left \Vert \begin R_ \ G_ \end \right \Vert _ \right).

\end factorization of the small subproblem in order to obtain the solution of our considered problem.