Many challenging tasks in sensor networks, including sensor calibration, ranking of nodes, monitoring, event region detection, collaborative filtering, collaborative signal processing, etc., can be formulated as a problem of solving a linear system of equations. Several recent works propose different distributed algorithms for solving these problems, usually by using linear iterative numerical ...

These notes outline a formal method for program verification of numerical computation. It forms the basis of the software package VPC in its initial phase of development. Much of the style of presentation is in the form of notes that outline the definitions and rules upon which VPC is based. The initial motivation of this project was to address some practical issues of computation, especially o...

This paper extends the singular value decomposition to a path of matrices E(t). An analytic singular value decomposition of a path of matrices E(t) is an analytic path of factorizations E(t) = X(t)S(t)Y (t)T where X(t) and Y (t) are orthogonal and S(t) is diagonal. To maintain di erentiability the diagonal entries of S(t) are allowed to be either positive or negative and to appear in any order....

The computation of tunneling probabilities in three dimensions is a numerical challenge, because the small transition probabilities associated with the overlap of exponentially vanishing wave function-tails require large computational accuracy. In scattering situations arising, e.g., in electron tunneling in metal-molecule-metal junctions, this is compounded by the need to provide a proper trun...