The problem of matrix inversion is central to many applications of Numerical Linear Algebra. When the matrix to invert is dense, little can be done to avoid the costly O(n) process of Gaussian Elimination. When the matrix is symmetric, one can use the Cholesky Factorization to reduce the work of inversion (still O(n), but with a smaller coefficient). When the matrix is both sparse and symmetric...

This research explores the double row layout problem (DRLP) that deals with how to place departments or machines on both sides of a central corridor. This type of layout problem is commonly observed in production and service facilities. Over the last 40 years, researchers have extensively studied a similar problem called the single row layout problem (SRLP) or one dimensional space allocation p...

Automated termination provers often use the following schema to prove that a program terminates: construct a relational abstraction of the program’s transition relation and then show that the relational abstraction is wellfounded. The focus of current tools has been on developing sophisticated techniques for constructing the abstractions while relying on known decidable logics (such as linear a...

Hierarchically-blocked non-linear storage layouts, such as the Morton ordering, have been shown to be a potentially attractive compromise between row-major and column-major for two-dimensional arrays. When combined with appropriate optimizations, Morton layout offers some spatial locality whether traversed rowor column-wise. However, for linear algebra routines with larger problem sizes, the la...

In the weighted rectangle stabbing problem we are given a grid in ]R2 consisting of columns and rows each having a positive integral weight, and a set of closed axis-parallel rectangles each having a positive integral demand. The rectangles are placed arbitrarily in the grid with the only assumption that each rectangle is intersected by at least one column and at least one row. The objective is...