Dynamic programming and minimal norm solutions of least squares problems

Safe Subspace Screening for Nuclear Norm Regularized Least Squares Problems

Nuclear norm regularization has been shown very promising for pursing a low rank matrix solution in various machine learning problems. Many efforts have been devoted to develop efficient algorithms for solving the optimization problem in nuclear norm regularization. Solving it for large-scale matrix variables, however, is still a challenging task since the complexity grows fast with the size of...

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations

Fast Enclosure for Solutions of Generalized Least Squares Problems∗

Fast algorithms for enclosing solutions of generalized least squares problems are proposed. To develop these algorithms, theories for obtaining error bounds on numerical solutions are established. The error bounds obtained by these algorithms are “verified” in the sense that all the possible rounding errors have been taken into account. A technique for obtaining smaller error bounds is introduc...

Least-squares Finite Element Approximations to Solutions of Interface Problems∗

A least-squares finite element method for second-order elliptic boundary value problems having interfaces due to discontinuous media properties is proposed and analyzed. Both Dirichlet and Neumann boundary data are treated. The boundary value problems are recast into a firstorder formulation to which a suitable least-squares principle is applied. Among the advantages of the method are that nonc...

Network Completion Using Dynamic Programming and Least-Squares Fitting

We consider the problem of network completion, which is to make the minimum amount of modifications to a given network so that the resulting network is most consistent with the observed data. We employ here a certain type of differential equations as gene regulation rules in a genetic network, gene expression time series data as observed data, and deletions and additions of edges as basic modif...