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A new spectral algorithm for reordering a sparse symmetric matrix to reduce its envelope size was described in 2]. The ordering is computed by associating a Laplacian matrix with the given matrix and then sorting the components of a speciied eigenvector of the Laplacian. In this paper we provide an analysis of the spectral envelope reduction algorithm. We(More)
This paper describes a very fast implementation of the m~n~mum degree algorithm, which is an effective heuristm scheme for fmding low-fill ordermgs for sparse positive definite matrices. This implementation has two important features: first, in terms of speed, it is competitive with other unplementations known to the authors, and, second, its storage(More)
T hroughout computing's long history and within the many forms of computers existing today, from hand-held smartphones to mammoth supercomputers, the one common denominator is the fixed-logic processor. In conventional computing, each application must be adapted to match the fixed structures, parallelism, functionality, and precision of the target(More)
—Multi-asset barrier contracts are path-dependent exotic options consisting of two or more underlying assets. As the dimensions of an option increase, so does the mathematical complexity of a closed form solution. Monte Carlo (MC) methods offer an attractive solution under such conditions. MC methods have an O(n-1/2) convergence rate irrespective of the(More)
— 123 With the ever-increasing demand for higher bandwidth and processing capacity of today's space exploration, space science, and defense missions, the ability to efficiently apply commercial-off-the-shelf (COTS) processors for on-board computing is now a critical need. In response to this need, NASA's New Millennium Program office has commissioned the(More)
Software for solving sparse systems of hnear equations typically involves fairly complicated data structures and storage management In many cases the user of such software simply wants to solve a system of equations, and should not have to be concerned with the way this storage management is actually done, or the way the matrix components are actually(More)