This article describes a fast direct solver (i.e., not iterative) for partial hierarchically semiseparable systems. This solver requires a storage of O(N logN) and has a computational complexity of O(N logN) arithmetic operations. The numerical benchmarks presented illustrate the method in the context of interpolation using radial basis functions. The key ingredients behind this fast solver are...

Surface smoothing applied to range/elevation data acquired using a variety of sources has been a very active area of research in computational vision over the past decade. Generalized splines have emerged as the single most popular approximation tool to this end. In this paper we present a new and fast algorithm for solving the surface smoothing problem using a membrane, a thin-plate, or a thin...

The Sherman-Woodbury-Morrison (SWM) formula gives an explicit formula for the inverse perturbation of a matrix in terms of the inverse of the original matrix and the perturbation. This formula is useful for numerical applications. We have produced similar results, giving an expression for the inverse of a matrix when the ith row and column are removed. However, our expression involves taking a ...

In this article, we consider some representations of {1, 3}, {1, 4}, {1, 2, 3} and {1, 2, 4}-inverses of a partitioned matrix M which are equivalent to some rank additivity conditions. We present some applications of these results to generalizations of the Sherman-Morrison-Woodbury-type formulae.

a r t i c l e i n f o a b s t r a c t Keywords: Three-dimensional computational fluid dynamics Particle methods Complex geometry Penalization Sherman–Morrison–Woodbury formula Krylov methods Non-homogeneous Stokes flow Biological flows Particle methods are very convenient to compute transport equations in fluid mechanics as their computational cost is linear and they are not limited by convecti...

The radar cross-section (RCS) of power lines has an important significance for detection the lines. method moments (MoM) can calculate RCS However, efficiency MoM is limited by time-consuming computing process, as well expensive storage overhead. In order to enhance and reduce calculation lines, we propose that combines characteristic mode (CM) with a Sherman–Morrison–Woodbury formula-based alg...

In this work, we introduce Log(v) 3LPF, a linear power flow solver for unbalanced three-phase distribution systems. 3LPF uses logarithmic transform of the voltage phasor to linearize AC equations around balanced case. We incorporate modeling ZIP loads, transformers, capacitor banks, switches and their corresponding controls express network in matrix-vector form. With scalability mind, special a...

This paper presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits the domain decomposition method and low-rank corrections. The domain decomposition approach decouples the matrix and once inverted, a low-rank approximation is applied by e...