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SOME RESULTS ON THE EXISTENCE, UNIQUENESS, AND COMPUTATION OF THE M-ESTIMATES OF MULTIVARIATE LOCATION AND SCATTER

SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING 1988年第2期9卷 354-362页

作者： TYLER, DE

The M-estimates of multivariate location and scatter are a class of robust alternatives to the sample mean vector and sample covariance matrix. They also have applications to bounded influence regression. There are a number of problems, though, which need to be resolved before they can become widely applicable. This paper addresses the problems of existence, uniqueness and computation of the M-estimates for finite sample sizes.

关键词： 62H12 62H10 62G05 bounded influence regression covariance matrix finite sample size fixed point algorithm sensitivity bound robust estimation

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GEOMETRIC algorithmS FOR THE NON-WHITENED ONE-UNIT LINEAR INDEPENDENT COMPONENT ANALYSIS PROBLEM

GEOMETRIC ALGORITHMS FOR THE NON-WHITENED ONE-UNIT LINEAR IN...

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15th IEEE/SP Workshop on Statistical Signal Processing

作者： Shen, Hao Diepold, Klaus Hueper, Knut Tech Univ Munich Inst Data Proc D-80290 Munich Germany Univ Wurzburg Dept Math D-97074 Wurzburg Germany

ISBN: (纸本)9781424427093

In this paper, we study the problem of one-unit linear Independent Component Analysis (ICA) without whitening. The FastICA algorithm is arguably the most popular algorithm for solving the whitened one-unit linear ICA problem. Although a modified FastICA has been already proposed to solve the non-whitened one-unit linear ICA problem, there is unfortunately no known analysis regarding its effectiveness and efficiency. In this work, the non-whitened FastICA algorithm is revisited and analyzed in the framework of geometric optimization algorithms. In this paper, a conjugate gradient (CG) algorithm for the non-whitened one-unit linear ICA problem is developed as well. Local convergence properties of both algorithms are discussed. Finally, local convergence performance of the algorithms is investigated by several numerical experiments.

关键词： Independent component analysis (ICA) non-whitening unit sphere fixed point algorithm conjugate gradient (CG) algorithm

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DEEP LEARNING BEAM OPTIMIZATION IN MILLIMETER-WAVE COMMUNICATION SYSTEMS 21

DEEP LEARNING BEAM OPTIMIZATION IN MILLIMETER-WAVE COMMUNICA...

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IEEE Statistical Signal Processing Workshop (SSP)

作者： Ismayilov, Rafail Cavalcante, Renato L. G. Stanczak, Slawomir Fraunhofer Heinrich Hertz Inst Berlin Germany Tech Univ Berlin Berlin Germany

ISBN: (纸本)9781728157672

We propose a method that combines fixed point algorithms with a neural network to optimize jointly discrete and continuous variables in millimeter-wave communication systems, so that the users' rates are allocated fairly in a well-defined sense. In more detail, the discrete variables include user-access point assignments and the beam configurations, while the continuous variables refer to the power allocation. The beam configuration is predicted from user-related information using a neural network. Given the predicted beam configuration, a fixed point algorithm allocates power and assigns users to access points so that the users achieve the maximum fraction of their interference-free rates. The proposed method predicts the beam configuration in a "one-shot" manner, which significantly reduces the complexity of the beam search procedure. Moreover, even if the predicted beam configurations are not optimal, the fixed point algorithm still provides the optimal power allocation and user-access point assignments for the given beam configuration.

关键词： Interference management millimeter-wave communication beamforming deep learning fixed point algorithm

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STATCOM Based Voltage and Frequency Regulator for Self Excited Induction Generator

STATCOM Based Voltage and Frequency Regulator for Self Excit...

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International Conference on Electrical, Electronics and System Engineering (ICEESE)

作者： Palwalia, D. K. Rajasthan Tech Univ Dept Elect Engn Kota India

ISBN: (纸本)9781479931781

This paper presents the digital design of a STATCOM based voltage and frequency regulator for self excited induction generator (SEIG) feeding linear and nonlinear loads. The SEIG have inherent poor voltage and frequency regulation. The voltage and frequency of the SEIG system depend upon the load current and power factor of the load for constant power operation with fixed excitation capacitor employing unregulated turbines. The performance of SEIG is largely affected by load harmonics. A current controlled voltage source inverter working as STATCOM is used for harmonic elimination, load balancing and it provides reactive power compensation. A DC chopper with dump load is connected across DC bus capacitor to regulate varying consumer load. The control algorithm has been co-simulated with processor in the loop (PIL) using TMS320F2812 fixed point DSP. The transient behaviour of SEIG-STATCOM system at different operating conditions such as application and removal of balanced, unbalanced and nonlinear load is investigated.

关键词： Self excited induction generator (SEIG) static compensator (STATCOM) processor in the loop (PIL) co-simulation digital signal processor (DSP) fixed point algorithm

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Estimation of common fixed points of SKC mappings and an application to fractional differential equations

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JOURNAL OF ANALYSIS 2024年第2期32卷 889-913页

作者： Ali, Javid Jubair, Mohd Aligarh Muslim Univ Dept Math Aligarh 202002 India Natl Inst Technol Dept Math Jalandhar India

This article aims to show that the classes of enriched nonexpansive mappings due to Berinde, the mappings satisfying Suzuki-(KC)-condition due to Karapinar and Tas and generalized nonexpansive mappings due to Hardy and Rogers do not imply each other. As an application of our main results, a common solution of the nonlinear fractional differential equations is approximated. Further, we establish some weak and strong convergence results for two Suzuki-(KC) mappings to approximate common fixed points by using S-type iterative algorithm in uniformly convex Banach spaces. For the valuation of our results, a couple of nontrivial numerical examples are also presented.

关键词： Suzuki-(KC)-mapping Enriched nonexpansive mapping Generalized nonexpansive mapping fixed point algorithm Common fixed point Fractional differential equation Uniformly convex Banach space

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REGULARIZED RICHARDSON-LUCY algorithm FOR RECONSTRUCTION OF POISSONIAN MEDICAL IMAGES

REGULARIZED RICHARDSON-LUCY ALGORITHM FOR RECONSTRUCTION OF ...

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8th IEEE International Symposium on Biomedical Imaging (ISBI) - From Nano to Macro

作者： Shaked, Elad Dolui, Sudipto Michailovich, Oleg V. Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada

ISBN: (纸本)9781424441280

The physical limitations of medical imaging devices together with the adverse effect of measurement noises tend to reduce the resolution and contrast of resulting diagnostic images. As a result, there is a need to preprocess the images before their interpretation by a medical practitioner. The present study is concerned with the case in which the images of interest are degraded by convolutional blur and Poisson noises. Such a situation is prevalent in many imaging modalities including PET, SPECT and confocal microscopy. To alleviate the image degradation, there exist a range of solution methods which are based on the principles originating from the fixed-point algorithm of Richardson and Lucy (RL). In this paper, we extend the RL algorithm to incorporate a constraint that requires the image of interest to be sparsely represented in the domain of a suitable linear transform. In this case, the positivity of the reconstructed image and its representation coefficients is ensured by using a positive valued dictionary of "representation atoms". The superiority of the proposed algorithm over some alternative reconstruction methods has been established through a series of numerical experiments.

关键词： Image deconvolution Poisson noise fixed point algorithm sparse representations

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The computation of a general equilibrium in a public goods economy

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Mathematical Programming 1978年第1期14卷 186-207页

作者： Richter, Donald K. Boston College Chestnut Hill MA United States

This paper presents an algorithm for computing approximations to a certain subset of Pareto optimal allocations in a public goods economy. Consumers are partitioned into a number of exogenous governmental jurisdictions, which provide public goods locally and raise revenue to cover their costs by means of a proportional wealth tax. The Pareto optimal allocations studied are consistent with profit maximization on the part of producers, and utility maximization over private goods bundles subject to after-tax budget constraints by consumers. The computational routine is based on the Scarf algorithm for computing fixed points. © 1978 The Mathematical Programming Society.

关键词： Computing Equilibria fixed point algorithm General Equilibrium Mathematical Economics Public Goods Economy Scarf algorithm

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Response and stability analysis of piecewise-linear oscillators under multi-forcing frequencies

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Nonlinear Dynamics 1992年第2期3卷 105-121页

作者： Choi, Sang-Kyu Noah, Sherif T. Dept. of Mechanical Engineering Texas A and M University College Station 77843-3123 Texas United States

Steady-state solutions of a piecewise-linear oscillator under multi-forcing frequencies are obtained using the fixed point algorithm (FPA). Stability analysis is also performed using the same technique. For the periodic solutions of a piecewise-linear oscillator with single forcing frequency, the harmonic balance method (HBM) is also used along with the FPA. Although both FPA and HBM generate accurate solutions, it is observed that the HBM failed to converge to solutions in the superharmonic range of the forcing frequency. The fixed point algorithm was also applied to the oscillator under multifrequency excitation. The algorithm proved to be very effective in obtaining torus solutions and in locating corresponding bifurcation thresholds. A piecewise-linear oscillator model of an offshore articulated loading platform (ALP) subjected to two incommensurate wave frequencies is found to exhibit chaotic behavior. A second order Poincaré mapping technique reveals the hidden fractal-like nature of the resulting chaotic response. A parametric study is performed for the response of the ALP. © 1992 Kluwer Academic Publishers.

关键词： bifurcation to chaos fixed point algorithm quasi-periodic response

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Convergence of Dynamic Harmonic Balance algorithm under maximum correntropy criterion

Convergence of Dynamic Harmonic Balance algorithm under maxi...

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International Conference on Inventive Computation Technologies (ICICT)

作者： Pujitha, Vanama Naga Rajani, Alugonda JNTUK Univ Coll Engn Dept ECE Kakinada India

ISBN: (纸本)9781509012855

Maximum correntropy criteria (MCC) has been exhibited a robustness against impulse noise by applying various area of signal process. MCC has been shown to be a rather robust adaption principle for adaptive system training in the presence of heavy-tailed non Gaussian noises. fixed point algorithms converge to the optimum solution more quickly for fixed signals. In this paper shows convergence of a Dynamic Harmonic Balance algorithms with sufficient condition and comparison between fixed point algorithm and Dynamic Harmonic Balance algorithm.

关键词： Maximum correntropy criteria fixed point algorithm Dynamic harmonic balance algorithm

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Comparing Disjunctive and Concise Approaches for Set-Guaranteed Estimation in Max-Plus Linear Systems 17

Comparing Disjunctive and Concise Approaches for Set-Guarant...

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17th IFAC Workshop on discrete Event Systems (WODES)

作者： Espindola-Winck, Guilherme Hardouin, Laurent Lhommeau, Mehdi Univ Lille CNRS Cent Lille UMR CRIStAL 9189 F-59000 Lille France Univ Angers LARIS SFR MATHSTIC F-49000 Angers France

This study compares an existing method with a novel approach for state estimation of Max-Plus Linear systems with bounded uncertainties. Traditional stochastic filtering does not apply to this system class, despite computable posterior probability density function (PDF) support. Existing literature suggests a limited scalability disjunctive approach using difference-bound matrices. To overcome this, we study an alternative method recently investigated in Mufid et al. (2022) using Satisfiability Modulo Theory (SMT) techniques, which are known to be NP-hard. We propose a concise method that utilizes a pseudo-polynomial time algorithm using max-plus algebra. We evaluate its efficiency against SMT techniques through numerical experiments involving sparse matrix multiplications for enhanced computational speed.

关键词： Max-Plus Linear Systems State-Estimation Satisfiability Modulo Theories fixed point algorithm

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