A smoothed aggregation multigrid method is presented for the numerical calculation of the stationary probability vector of an irreducible sparse Markov chain. It is shown how smoothing the interpolation and restriction operators can dramatically increase the efficiency of aggregation multigrid methods for Markov chains that have been proposed in the literature. The proposed smoothing approach i...

We give a convergence estimate for a Petrov-Galerkin Algebraic Multigrid method. In this method, the prolongations are defined using the concept of smoothed aggregation while the restrictions are simple aggregation operators. The analysis is carried out by showing that these methods can be interpreted as variational Ritz-Galerkin ones using modified transfer and smoothing operators. The estimat...

Abstract. The local L-mapping property of Fourier integral operators has been established in Hörmander [14] and in Eskin [12]. In this paper, we treat the global L -boundedness for a class of operators that appears naturally in many problems. As a consequence, we will improve known global results for several classes of pseudodifferential and Fourier integral operators, as well as extend previou...

Unions of graph multiplier operators are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators. The proposed method features approximations of the graph multipliers by shifted Chebyshev polynomials, whose recurrence relations make them readily amenable to distributed computation. We...

Newly developed combinatorial Laplacians and curvature operators for grayscale, as well as color images are tested on 2D synthetic and natural images. This novel approach is based upon more general concepts developed by R. Forman and is inspired by the Bochner-Weitzeböck formula which is an essential identity in Riemannian Geometry. After the presentation of the operators as they operate on ima...