The Experts below are selected from a list of 18642 Experts worldwide ranked by ideXlab platform
Samuel Cheng - One of the best experts on this subject based on the ideXlab platform.
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Implementing distributed graph filters by Elementary Matrix decomposition
arXiv: Signal Processing, 2019Co-Authors: Samuel ChengAbstract:In this letter, we consider the implementation problem of distributed graph filters, where each node only has access to the signals of the current and its neighboring nodes. By using Gaussian elimination, we show that as long as the graph is connected, we can implement any graph filter by decomposing the filter into a product of directly implementable filters, filters that only use the signals at the current and neighboring nodes as inputs. We have also included a concrete example as an illustration.
Bogdan Szafraniec - One of the best experts on this subject based on the ideXlab platform.
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Elementary Matrix method for dispersion analysis in optical systems
Journal of Lightwave Technology, 2010Co-Authors: Douglas M Baney, Bogdan SzafraniecAbstract:In this paper, dispersion analysis of optical components and systems is presented using a formalism based on the Elementary matrices and the N-Matrix, first described by Jones. This approach readily incorporates both phase and amplitude dispersion in a generalized dispersion framework. The method simplifies the analysis of the combined effects of group delay, differential group delay, amplitude slope, and differential amplitude slope as compared to traditional Jones Matrix methods. Higher order polarization-mode dispersion and the effects of concatenation are presented along with a discussion of measurement principles. The application of the Elementary Matrix concept to Mueller Matrix methods in Stokes space is also discussed.
Willis Lin - One of the best experts on this subject based on the ideXlab platform.
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convergence analysis of structure preserving doubling algorithms for riccati type Matrix equations
SIAM Journal on Matrix Analysis and Applications, 2006Co-Authors: Willis LinAbstract:In this paper, we introduce the doubling transformation, a structure-preserving transformation for symplectic pencils, and present its basic properties. Based on these properties, a unified convergence theory for the structure-preserving doubling algorithms for a class of Riccati-type Matrix equations is established, using only Elementary Matrix theory.
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a structure preserving doubling algorithm for nonsymmetric algebraic riccati equation
Numerische Mathematik, 2006Co-Authors: Xiaoxia Guo, Willis LinAbstract:In this paper, we propose a structure-preserving doubling algorithm (SDA) for the computation of the minimal nonnegative solution to the nonsymmetric algebraic Riccati equation (NARE), based on the techniques developed for the symmetric cases. This method allows the simultaneous approximation to the minimal nonnegative solutions of the NARE and its dual equation, requiring only the solutions to two linear systems and several Matrix multiplications per iteration. Similar to Newton's method and the fixed-point iteration methods for solving NAREs, we also establish global convergence for SDA under suitable conditions, using only Elementary Matrix theory. We show that sequences of matrices generated by SDA are monotonically increasing and quadratically convergent to the minimal nonnegative solutions of the NARE and its dual equation. Numerical experiments show that the SDA algorithm is feasible and effective, and outperforms Newton's iteration and the fixed-point iteration methods.
Marc Masdeu - One of the best experts on this subject based on the ideXlab platform.
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Elementary Matrix decomposition and the computation of darmon points with higher conductor
Mathematics of Computation, 2014Co-Authors: Xavier Guitart, Marc MasdeuAbstract:We extend the algorithm of (DG02) and (DP06) for computing p-adic Darmon points on elliptic curves to the case of composite conductor. We also extend the algorithm of (DL03) for computing ATR Darmon points to treat curves of nontrivial conductor. Both cases involve an algorithmic decomposition into Elementary matrices in congruence subgroups 1(N) for ideals N in certain rings of S-integers. We use these extensions to provide additional evidence in support of the conjectures on the rationality of Darmon points.
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Elementary Matrix decomposition and the computation of darmon points with higher conductor
arXiv: Number Theory, 2012Co-Authors: Xavier Guitart, Marc MasdeuAbstract:We extend the algorithm of Darmon-Green and Darmon-Pollack for computing p-adic Darmon points on elliptic curves to the case of composite conductor. We also extend the algorithm of Darmon-Logan for computing ATR Darmon points to treat curves of nontrivial conductor. Both cases involve an algorithmic decomposition into Elementary matrices in congruence subgroups {\Gamma}(N) for ideals N in certain rings of S-integers. We use these extensions to provide additional evidence in support of the conjectures on the rationality of Darmon points.
Douglas M Baney - One of the best experts on this subject based on the ideXlab platform.
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Elementary Matrix method for dispersion analysis in optical systems
Journal of Lightwave Technology, 2010Co-Authors: Douglas M Baney, Bogdan SzafraniecAbstract:In this paper, dispersion analysis of optical components and systems is presented using a formalism based on the Elementary matrices and the N-Matrix, first described by Jones. This approach readily incorporates both phase and amplitude dispersion in a generalized dispersion framework. The method simplifies the analysis of the combined effects of group delay, differential group delay, amplitude slope, and differential amplitude slope as compared to traditional Jones Matrix methods. Higher order polarization-mode dispersion and the effects of concatenation are presented along with a discussion of measurement principles. The application of the Elementary Matrix concept to Mueller Matrix methods in Stokes space is also discussed.