Critical points of matrix least squares distance functions

Critical Points for Least - Squares ProblemsInvolving

This paper deals with nonlinear least-squares problems involving the tting to data of parameterized analytic functions. For generic regression data, a general result establishes the countability, and under stronger assumptions niteness, of the set of functions giving rise to critical points of the quadratic loss function. In the special case of what are usually called \single-hidden layer neura...

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations

Critical points for least-squares problems involving certain analytic functions, with applications to sigmoidal nets

This paper deals with nonlinear least-squares problems involving the fitting to data of parameterized analytic functions. For generic regression data, a general result establishes the countability, and under stronger assumptions finiteness, of the set of functions giving rise to critical points of the quadratic loss function. In the special case of what are usually called “single-hidden layer n...

On Least Squares Euclidean Distance Matrix Approximation and Completion

The Euclidean distance matrix approximation problem as well as the completion problem have received a lot of attention in recent years because of their many important applications. In contrast to the many interesting but often sophisticated algorithms proposed in the literature, this paper offers a relatively straightforward procedure that can tackle both problems by the same framework. The loc...

Least-Squares Covariance Matrix Adjustment

We consider the problem of finding the smallest adjustment to a given symmetric n × n matrix, as measured by the Euclidean or Frobenius norm, so that it satisfies some given linear equalities and inequalities, and in addition is positive semidefinite. This least-squares covariance adjustment problem is a convex optimization problem, and can be efficiently solved using standard methods when the ...