Path-following methods for primal-dual active set strategies requiring a regularization parameter are introduced. Existence of a path and its differentiability properties are analyzed. Monotonicity and convexity of the ...

We describe a linear-time algorithm for solving the molecular distance geometry problem with exact distances between all pairs of atoms. This problem needs to be solved in every iteration of general distance geometry ...

It is well-known by now that under suitable conditions L1 minimization can recover sparse solutions to under-determined linear systems of equations. More precisely, by solving the convex optimization problem min{||x||1 : ...

The stability number for a given graph G is the size of a maximum stable set in G. The Lovasz theta number provides an upper bound on the stability number and can be computed as the optimal value of the Lovasz semidefinite ...

The restarted Arnoldi algorithm, implemented in the ARPACK software library and MATLAB's eigs command, is among the most common means of computing select eigenvalues and eigenvectors of a large, sparse matrix. To assist ...

The emerging field of molecular electronics seeks to create computational function from individual molecules or arrays of molecules. These nanoscale devices would then enable the production of faster, denser, cheaper ...

Removing the minimum number of vertices or points from a square lattice such that no square path exists is known as the square path problem. Finding this number as the size of the lattice increases is not so trivial. Results ...

It is well-known by now that L1 minimization can help recover sparse solutions to under-determined linear equations or sparsely corrupted solutions to over-determined equations, and the two problems are equivalent under ...

This thesis describes a flexible framework for abstract numerical algorithms which treats algorithms as objects and makes them reusable, composable, and modifiable. These algorithm objects are implemented using the Rice ...

Arnoldi's method is often used to compute a few eigenvalues and eigenvectors of large, sparse matrices. When the eigenvalues of interest are not dominant or well-separated, this method may suffer from slow convergence. ...