Butterfly Factorization

The paper introduces the butterfly factorization as a data-sparse approximation for the matrices that satisfy a complementary low-rank property. The factorization can be constructed efficiently if either fast algorithms for applying the matrix and its adjoint are available or the entries of the matrix can be sampled individually. For an $N \times N$ matrix, the resulting factorization is a product of $O(\log N)$ sparse matrices, each with $O(N)$ non-zero entries. Hence, it can be applied rapidly in $O(N\log N)$ operations. Numerical results are provided to demonstrate the effectiveness of the butterfly factorization and its construction algorithms

A hybrid recursive multilevel incomplete factorization preconditioner for solving general linear systems

In this paper we introduce an algebraic recursive multilevel incomplete factorization preconditioner, based on a distributed Schur complement formulation, for solving general linear systems. The novelty of the proposed method is to combine factorization techniques of both implicit and explicit type, recursive combinatorial algorithms, multilevel mechanisms and overlapping strategies to maximize sparsity in the inverse factors and consequently reduce the factorization costs. Numerical experiments demonstrate the good potential of the proposed solver to precondition effectively general linear systems, also against other state-of-the-art iterative solvers of both implicit and explicit form

On the orbit determination problem

Various important aspects of the satellite orbit determination problem are critically discussed with a view to emphasizing the importance of a wise choice of suitable system models, coordinates sets, and estimators. We describe several aspects of the orbit determination process and also review much of the available literature on the application of Kalman filter type algorithms to the problem of near-Earth, geosynchronous, and deep-space mission type orbit determination are also addressed. It is believed that this review with a touch of tutorial will enable engineers and scientists to arrive at an orbit determination methodology (ODM) that will have attributes of good numerical stability, efficiency, and precision in orbit estimation

ADAPTIVE AND NONLINEAR SIGNAL PROCESSING

1996/1997X Ciclo1967Versione digitalizzata della tesi di dottorato cartacea