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newton algorithm on Constraint Manifolds and the 5-Electron Thomson Problem

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2017年第2期173卷 563-583页

作者： Birtea, Petre Comanescu, Dan West Univ Timisoara Dept Math Timisoara Romania

We give a description of numerical newton algorithm on a constraint manifold using only the ambient coordinates (usually Euclidean coordinates) and the geometry of the constraint manifold. We apply the numerical newton algorithm on a sphere in order to find the critical configurations of the 5-electron Thomson problem. As a result, we find a new critical configuration of a regular pentagonal type. We also make an analytical study of the critical configurations found previously and determine their nature using Morse-Bott theory. The last section contains an analytical study of critical configurations for Riesz s-energy of 5-electron on a sphere, and their bifurcation behavior is pointed out.

关键词： newton algorithm Constraint manifold Hessian operator Morse theory 5-Electron Thomson problem Riesz s-energy

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A time-varying newton algorithm for adaptive subspace tracking

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MATHEMATICS AND COMPUTERS IN SIMULATION 2008年第4期79卷 1324-1345页

作者： Baumann, M. Helmke, U. Univ Wurzburg Inst Math D-97074 Wurzburg Germany

We propose a general framework for tracking the zeros of a time-varying gradient vector field on Riemannian manifolds. Thus, a differential equation, called the time-varying newton flow, is introduced, whose solutions asymptotically converge to a time-varying family of critical points of the corresponding cost function. A discretization of the differential equation leads to a recursive update scheme for the time-varying critical point. As an application of such techniques we develop new algorithms for computing the principal and minor subspace of a time-varying family of symmetric matrices. Using a convenient local parameterization of the Grassmann manifold, we derive simple expressions for the subspace tracking schemes. Key benefits of the algorithms are (a) the reduced complexity aspects due to efficient parameterizations of the Grassmannian and (b) their guaranteed accuracy during all iterates. Numerical simulations illustrate the feasibility of the approach. (C) 2008 IMACS. Published by Elsevier B.V. All tights reserved.

关键词： Adaptive subspace tracking Eigenvalue methods newton algorithm Riemannian metrics Grassmann manifolds

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Active-Set newton algorithm for Overcomplete Non-Negative Representations of Audio

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IEEE TRANSACTIONS ON AUDIO SPEECH AND LANGUAGE PROCESSING 2013年第11期21卷 2277-2289页

作者： Virtanen, Tuomas Gemmeke, Jort Florent Raj, Bhiksha Tampere Univ Technol Dept Signal Proc Tampere 33720 Finland Katholieke Univ Leuven Ctr Proc Speech & Images Dept Elect Engn B-3000 Louvain Belgium Carnegie Mellon Univ Sch Comp Sci Language Technol Inst Pittsburgh PA 15213 USA

This paper proposes a computationally efficient algorithm for estimating the non-negative weights of linear combinations of the atoms of large-scale audio dictionaries, so that the generalized Kullback-Leibler divergence between an audio observation and the model is minimized. This linear model has been found useful in many audio signal processing tasks, but the existing algorithms are computationally slow when a large number of atoms is used. The proposed algorithm is based on iteratively updating a set of active atoms, with the weights updated using the newton method and the step size estimated such that the weights remain non-negative. algorithm convergence evaluations on representing audio spectra that are mixtures of two speakers show that with all the tested dictionary sizes the proposed method reaches a much lower value of the divergence than can be obtained by conventional algorithms, and is up to 8 times faster. A source separation evaluation revealed that when using large dictionaries, the proposed method produces a better separation quality in less time.

关键词： Acoustic signal analysis audio source separation convex optimization newton algorithm non-negative matrix factorization sparse coding sparse representation supervised source separation

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Three-Dimensional Ultra-Short Base Line Based Underwater Acoustical Localization Utilizing Modified newton algorithm

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IEEE ACCESS 2021年 9卷 80671-80681页

作者： Li, Xiang Liu, Xin Qu, Long Lou, Yi Sun, Sibo Harbin Engn Univ Acoust Sci & Technol Lab Harbin 150001 Peoples R China Harbin Engn Univ Key Lab Marine Informat Acquisit & Secur Minist Ind & Informat Technol Harbin 150001 Peoples R China China State Shipbldg Corp Ltd 703 Res Inst Harbin 150001 Peoples R China Harbin Engn Univ Coll Underwater Acoust Engn Harbin 150001 Peoples R China

The ultra-short base line (USBL) is a widely used technique in achieving the underwater acoustic localization (UWAL). Aimed at increasing the localization precision, we propose a three-dimensional (3-D) USBL based UWAL method utilizing the modified newton algorithm. Firstly, a modified newton algorithm is proposed by introducing the singular value factor to address the non-convergence problem, which dramatically deteriorate the localization precision in the traditional newton algorithm. Secondly, a localization node selection algorithm is presented to optimize the localization precision and reduce the computational burden. Moreover, the localization precision analysis is implemented to evaluate the theoretical performance of the method. Finally, simulation and lake trial results prove the effectiveness of the method.

关键词： Location awareness Mathematical model Direction-of-arrival estimation Noise measurement Estimation Sea measurements Robustness Underwater acoustic localization (UWAL) ultra short base line (USBL) direction of arrival (DOA) newton algorithm

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Analysis of an efficient parallel implementation of active-set newton algorithm

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JOURNAL OF SUPERCOMPUTING 2019年第3期75卷 1298-1309页

作者： San Juan Sebastian, Pablo Virtanen, Tuomas Garcia-Molla, Victor M. Vidal, Antonio M. Univ Politecn Valencia Dept Informat Syst & Comp Valencia Spain Tampere Univ Technol Dept Signal Proc Tampere Finland

This paper presents an analysis of an efficient parallel implementation of the active-set newton algorithm (ASNA), which is used to estimate the nonnegative weights of linear combinations of the atoms in a large-scale dictionary to approximate an observation vector by minimizing the Kullback-Leibler divergence between the observation vector and the approximation. The performance of ASNA has been proved in previous works against other state-of-the-art methods. The implementations analysed in this paper have been developed in C, using parallel programming techniques to obtain a better performance in multicore architectures than the original MATLAB implementation. Also a hardware analysis is performed to check the influence of CPU frequency and number of CPU cores in the different implementations proposed. The new implementations allow ASNA algorithm to tackle real-time problems due to the execution time reduction obtained.

关键词： newton algorithm Convex optimization Sparse representation Multicore Parallel computing

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An improved newton algorithm based on finite element analysis for extracting the Brillouin scattering spectrum features

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MEASUREMENT 2014年第1期51卷 310-314页

作者： Zhang, Yanjun Yu, Chunjuan Fu, Xinghu Li, Da Jia, Wei Bi, Weihong Yanshan Univ Sch Informat Sci & Engn Qinhuangdao 066004 Peoples R China Yanshan Univ Key Lab Special Fiber & Fiber Sensor Hebei Prov Qinhuangdao 066004 Peoples R China

In the distributed optical fiber sensing system based on Brillouin scattering, the photodetector offers the low signal-to-noise ratio (SNR) and can hardly demodulate complicated information. An improved newton algorithm based on finite element analysis (FEA-newton algorithm) is proposed to extract the estimated parameters of Brillouin scattering spectrum from noisy signals accurately. By using the FEA-newton algorithm, the relationship of the linewidth vs center frequency shift error and SNR vs center frequency shift error are both analyzed and the Brillouin center frequency shifts are extracted. Within a certain range of initial value, the accuracy of the newton and FEA-newton algorithms are compared. The measured Brillouin shift of FEA-newton algorithm is match with theoretical values. The FEA-newton algorithm is more preferably to extract the Brillouin scattering spectrum features. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Distributed fiber sensors Brillouin scattering spectrum newton algorithm Finite element analysis

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Blind Source Separation Using Decoupled Relative newton algorithm

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IEEE SIGNAL PROCESSING LETTERS 2012年第9期19卷 567-570页

作者： Li, Xi-Lin Fortemedia Inc Sunnyvale CA 94085 USA

A decoupled relative newton algorithm is proposed for the matrix optimization problem encountered in blind source separation (BSS) and independent component analysis (ICA). The algorithm decouples the matrix optimization problem into a series of small vector optimization problems. The nonsingularity of separation matrix enables a simple and efficient relative newton learning algorithm for the vector optimization problems. Simulation results are reported to confirm its superior performance.

关键词： Blind source separation independent component analysis newton algorithm relative gradient

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ACTIVE-SET newton algorithm FOR NON-NEGATIVE SPARSE CODING OF AUDIO

ACTIVE-SET NEWTON ALGORITHM FOR NON-NEGATIVE SPARSE CODING O...

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IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Virtanen, Tuomas Raj, Bhiksha Gemmeke, Jort F. Van Hamme, Hugo Tampere Univ Technol Dept Signal Proc FIN-33101 Tampere Finland Carnegie Mellon Univ Language Technol Inst Pittsburgh PA 15213 USA Katholieke Univ Leuven Dept Elect Engn Leuven Belgium

ISBN: (纸本)9781479928934

We propose a new algorithm to efficiently obtain non-negative sparse representations for audio. The spectrum of an audio signal is represented as a sparse linear combination of atoms taken from an overcomplete dictionary. The algorithm is based on minimizing the generalized Kullback-Leibler divergence between an observed magnitude spectrum and a non-negative linear combination of atoms, plus an l(1) regularization term. The proposed method consists of an active-set method that iteratively updates a set of active atoms that have non-zero weights, using a newton step where the weights of the active atoms are updated. The proposed method was evaluated using mixtures of two speakers, and it was shown to yield more than 10 times faster convergence in comparison to an established algorithm based on multiplicative update rules. Moreover, the l(1) regularization was found to decrease the computation time and to improve the source separation performance.

关键词： sound source separation non-negative matrix factorization newton algorithm convex optimization sparse coding

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newton algorithm for Hamiltonian characterization in quantum control

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JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 2014年第26期47卷 265302-265302页

作者： Ndong, M. Salomon, J. Sugny, D. Univ Bourgogne CNRS Lab Interdisciplinaire Carnot Bourgogne ICB UMR 6303 F-21078 Dijon France Univ Paris 09 UMR CNRS 7534 CEREMADE F-75775 Paris 16 France

We propose a newton algorithm to characterize the Hamiltonian of a quantum system interacting with a given laser field. The algorithm is based on the assumption that the evolution operator of the system is perfectly known at a fixed time. The computational scheme uses the Crank-Nicholson approximation to explicitly determine the derivatives of the propagator with respect to the Hamiltonians of the system. In order to globalize this algorithm, we use a continuation method that improves its convergence properties. This technique is applied to a two-level quantum system and to a molecular one with a double-well potential. The numerical tests show that accurate estimates of the unknown parameters are obtained in some cases. We discuss the numerical limits of the algorithm in terms of the basin of convergence and the non-uniqueness of the solution.

关键词： quantum control newton algorithm identification method

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A Novel Method for Microphone Channel Frequency Response Calibration Based on newton algorithm

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2023年 72卷 1页

作者： Wang, Ziyi Zhao, Zhao Xu, Zhiyong Nanjing Univ Sci & Technol Sch Elect & Opt Engn Nanjing 210094 Peoples R China

Microphone arrays are widely applied in practical applications. In an array, each channel conventionally contains an acoustic sensor and a following signal conditioning circuit (SCC). Frequency response mismatches among channels will adversely affect array's overall performance. Existing calibration methods provide promising results;however, their accuracy varies considerably across full frequency band and the passband bandwidth shrinkage problem also arises. To address these problems, we propose a novel calibration method based on newton algorithm. The proposed method cascades calibration filters after channel output signals allowing the frequency response calibration to be equivalent to the optimization of calibration filter coefficients. First, all uncalibrated channels' bandwidths are analyzed using a chirp calibration signal, resulting in appropriate construction of the desired output. Next, a spectrum mean square error criterion between each channel output and the desired signal is utilized to formulate the frequency response mismatch. Finally, we employ newton algorithm to design the calibration filter coefficients corresponding to each channel. Explicit mathematical derivation is provided. Since the cost function is quadratic, expressions of the constant Hessian matrix and its inverse are derived. Furthermore, the inverse Hessian can be efficiently computed using spectral coefficients of channel outputs. Simulation results reveal that the proposed method significantly outperforms the state-of-the-art calibration approaches in terms of calibration accuracy, calibrated passband bandwidth performance, and convergence rate. Real-world experiments also verify its effectiveness.

关键词： Calibration Bandwidth Frequency response Passband Loudspeakers Microphone arrays Filtering algorithms Frequency response calibration microphone channel newton algorithm

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