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Multigrid methods have proven to be an invaluable tool to efficiently solve large sparse linear systems arising in the discretization of partial differential equations (PDEs). Algebraic multigrid methods and in particular adaptive algebraic…

Numerical Analysis · Mathematics 2020-04-27 Hanno Gottschalk , Karsten Kahl

Interpolation by various types of splines is the standard procedure in many applications. In this paper we shall discuss harmonic spline "interpolation" (on the lines of a grid) as an alternative to polynomial spline interpolation (at…

Numerical Analysis · Mathematics 2011-01-17 Yuliya Babenko , Tatyana Leskevich

This paper characterizes hierarchical clustering methods that abide by two previously introduced axioms -- thus, denominated admissible methods -- and proposes tractable algorithms for their implementation. We leverage the fact that, for…

Machine Learning · Computer Science 2016-07-22 Gunnar Carlsson , Facundo Mémoli , Alejandro Ribeiro , Santiago Segarra

This papers highlights the benefit of coordinating resources on mulitple active distribution feeders during severe long duration outages through multi-microgrid formation. A graph-theory based multi-microgrid formation algorithm is…

Systems and Control · Electrical Eng. & Systems 2023-11-28 Valliappan Muthukaruppan , Rongxing Hu , Ashwin Shirsat , Mesut Baran , Ning Lu , Wenyuan Tang , David Lubkeman

In this work, we investigate a model order reduction scheme for polynomial parametric systems. We begin with defining the generalized multivariate transfer functions for the system. Based on this, we aim at constructing a reduced-order…

Numerical Analysis · Mathematics 2019-04-29 Peter Benner , Pawan Goyal

The aim of this paper is to extend the approximate quasi-interpolation on a uniform grid by dilated shifts of a smooth and rapidly decaying function on a uniform grid to scattered data quasi-interpolation. It is shown that high order…

Numerical Analysis · Mathematics 2007-05-23 F. Lanzara , V. Maz'ya , G. Schmidt

In this paper we define a family of nonlinear, stationary, interpolatory subdivision schemes with the capability of reproducing conic shapes including polynomials upto second order. Linear, non-stationary, subdivision schemes do also…

Numerical Analysis · Mathematics 2024-12-03 Rosa Donat , Sergio López-Ureña

Sparse incidence tensors can represent a variety of structured data. For example, we may represent attributed graphs using their node-node, node-edge, or edge-edge incidence matrices. In higher dimensions, incidence tensors can represent…

Machine Learning · Computer Science 2020-08-13 Marjan Albooyeh , Daniele Bertolini , Siamak Ravanbakhsh

Multi-hop communication with the aid of large-scale antenna arrays will play a vital role in future emergence communication systems. In this paper, we investigate amplify-and-forward based and multiple-input multiple-output assisted…

Information Theory · Computer Science 2020-01-14 Chengwen Xing , Xin Zhao , Shuai Wang , Wei Xu , Soon Xin Ng , Sheng Chen

Extremely large-scale multiple-input multiple-output (XL-MIMO) systems are pivotal to next-generation wireless communications, where dynamic RF chain architectures offer enhanced performance. However, efficient precoding in such systems…

Signal Processing · Electrical Eng. & Systems 2025-09-25 Jiayi Lu , Jiayi Zhang , Hao Lei , Huahua Xiao , Bo Ai , Derrick Wing Kwan Ng

We present an approach to constructing a practical coarsening algorithm and interpolation operator for the algebraic multigrid (AMG) method, tailored towards systems of partial differential equations (PDEs) with large near-kernels, such as…

Numerical Analysis · Mathematics 2025-01-28 James Brannick , Robert Falgout , Karsten Kahl , Jacob Schroder , Taoli Shen

We study non-conforming grid interfaces for summation-by-parts finite difference methods applied to partial differential equations with second derivatives in space. To maintain energy stability, previous efforts have been forced to accept a…

Numerical Analysis · Mathematics 2020-02-11 Martin Almquist , Siyang Wang , Jonatan Werpers

This work concerns the modeling of radiative transfer in anisotropic turbid media using diffusion theory. A theory for the relationship between microscopic scattering properties (i.e., an arbitrary differential scattering cross-section) and…

Optics · Physics 2014-08-14 Erik Alerstam

Based on previous work we extend a primal-dual semi-smooth Newton method for minimizing a general $L^1$-$L^2$-$TV$ functional over the space of functions of bounded variations by adaptivity in a finite element setting. For automatically…

Numerical Analysis · Mathematics 2025-02-19 Martin Alkämper , Stephan Hilb , Andreas Langer

We consider anisotropic heat flow with extreme anisotropy, as arises in magnetized plasmas for fusion applications. Such problems pose significant challenges in both obtaining an accurate approximation as well in the construction of an…

Numerical Analysis · Mathematics 2024-12-12 Maria Vasilyeva , Golo A. Wimmer , Ben S. Southworth

Multilevel, multiarea, and hierarchically interconnected electrical power grids confront substantial challenges with the increasing integration of many volatile energy resources. The traditional isolated operation of interconnected power…

Systems and Control · Electrical Eng. & Systems 2020-07-07 Chenhui Lin , Wenchuan Wu

We study the supervised clustering problem under the two-component anisotropic Gaussian mixture model in high dimensions and in the non-asymptotic setting. We first derive a lower and a matching upper bound for the minimax risk of…

Statistics Theory · Mathematics 2021-11-16 Stanislav Minsker , Mohamed Ndaoud , Yiqiu Shen

In this paper, a new class of \emph{Taylor-accelerated neural network interpolation operators} is introduced on quasi-uniform irregular grids. These operators improve existing neural network interpolation operators by incorporating Taylor…

Numerical Analysis · Mathematics 2026-02-11 Sachin Saini

A self-learning algebraic multigrid method for dominant and minimal singular triplets and eigenpairs is described. The method consists of two multilevel phases. In the first, multiplicative phase (setup phase), tentative singular triplets…

Numerical Analysis · Mathematics 2011-02-07 Hans De Sterck

We study an abstract family of asymptotically degenerating variational problems. Those are natural generalisations of families of problems emerging upon application of a rescaled Floquet-Bloch-Gelfand transform to resolvent problems for…

Analysis of PDEs · Mathematics 2025-08-27 Shane Cooper , Ilia Kamotski , Valery P. Smyshlyaev