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lanczos-type algorithms with embedded interpolation and extrapolation models for solving large-scale systems of linear equations

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INTERNATIONAL JOURNAL OF COMPUTING SCIENCE AND MATHEMATICS 2019年第5期10卷 429-442页

作者： Maharani, Maharani Larasati, Niken Salhi, Abdellah Khan, Wali Mashwani Univ Jenderal Soedirman Dept Math Purwokerto Jawa Tengah Indonesia Univ Essex Dept Math Sci Wivenhoe Pk Colchester CO4 3YS Essex England Univ Sci & Technol Dept Math Kohat Pakistan

The new approach to combating instability in lanczos-type algorithms for large-scale problems is proposed. It is a modification of so called the embedded interpolation and extrapolation model in lanczos-type algorithms (EIEMLA), which enables us to interpolate the sequence of vector solutions generated by a lanczos-type algorithm entirely, without rearranging the position of the entries of the vector solutions. The numerical results show that the new approach performs more effectively than the EIEMLA. In fact, we extend this new approach on the use of a restarting framework to obtain the convergence of lanczos algorithms accurately. This kind of restarting challenges other existing restarting strategies in lanczos-type algorithms.

关键词： lanczos algorithm interpolation extrapolation systems of linear equations embedded interpolation and extrapolation model in lanczos-type algorithms EIEMLA restarting strategy

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Indefinite Ruhe's Variant of the Block lanczos Method for Solving the Systems of Linear Equations

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ADVANCES IN MATHEMATICAL PHYSICS 2020年第1期2020卷

作者： Kamalvand, M. Ghasemi Asil, K. Niazi Lorestan Univ Dept Math Khorramabad Iran

In this paper, we equip Cn with an indefinite scalar product with a specific Hermitian matrix, and our aim is to develop some block Krylov methods to indefinite mode. In fact, by considering the block Arnoldi, block FOM, and block lanczos methods, we design the indefinite structures of these block Krylov methods;along with some obtained results, we offer the application of this methods in solving linear systems, and as the testifiers, we design numerical examples.

关键词： Linear system Hermitian matrix lanczos algorithm Linear equation

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Convergence Analysis of Krylov Subspace Spectral Methods for Reaction-Diffusion Equations

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JOURNAL OF SCIENTIFIC COMPUTING 2019年第3期78卷 1768-1789页

作者： Sheikholeslami, Somayyeh Lambers, James V. Walker, Carley Beaumont Hlth Dept Radiat Oncol Royal Oak MI 48073 USA Univ Southern Mississippi Sch Math & Nat Sci 118 Coll Dr 5043 Hattiesburg MS 39406 USA

Krylov subspace spectral (KSS) methods are explicit time-stepping methods for partial differential equations that are designed to extend the advantages of Fourier spectral methods, when applied to constant-coefficient problems, to the variable-coefficient case. This paper presents a convergence analysis of a first-order KSS method applied to a system of coupled equations for modeling first-order photobleaching kinetics. The analysis confirms what has been observed in numerical experimentsthat the method is unconditionally stable and achieves spectral accuracy in space. Further analysis shows that this unconditional stability is not limited to the case in which the leading coefficient is constant.

关键词： lanczos algorithm Spectral methods Gauss quadrature FRAP Photobleaching kinetics equation

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An application of the discrete-time Toda lattice to the progressive algorithm by lanczos and related problems

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JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 2018年第17期51卷 174001-174001页

作者： Nakamura, Yoshimasa Sekido, Hiroto Kyoto Univ Grad Sch Informat Dept Appl Math & Phys Kyoto 6068501 Japan

The finite or the semi-infinite discrete-time Toda lattice has many applications to various areas in applied mathematics. The purpose of this paper is to review how the Toda lattice appears in the lanczos algorithm through the quotient-difference algorithm and its progressive form (pqd). Then a multistep progressive algorithm (MPA) for solving linear systems is presented. The extended lanczos parameters can be given not by computing inner products of the extended lanczos vectors but by using the pqd algorithm with highly relative accuracy in a lower cost. The asymptotic behavior of the pqd algorithm brings us some applications of MPA related to eigenvectors.

关键词： discrete-time Toda lattice qd algorithm lanczos algorithm multistep progressive algorithm

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A Low Complexity Greedy algorithm for Dynamic Subarrays in mmWave MIMO Systems 90

A Low Complexity Greedy Algorithm for Dynamic Subarrays in m...

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90th IEEE Vehicular Technology Conference (IEEE VTC-Fall)

作者： Xu, Ke Zheng, Fu-Chun Cao, Pan Xu, Hongguang Zhu, Xu Harbin Inst Technol Shenzhen Sch Elect & Informat Engn Shenzhen Peoples R China Univ Hertfordshire Sch Engn & Technol Hatfield AL10 9AB Herts England Pengcheng Lab Shenzhen Peoples R China

ISBN: (纸本)9781728112206

For a mmWave multiple input multiple output (MIMO) system, the hybrid precoding scheme is of great interest due to its lower power consumption and hardware cost, where a smaller number of RF chains are used to feed a larger scale of antenna array. In this paper we consider a flexible architecture where RF chains and antennae can be dynamically connected, and propose a greedy algorithm to achieve dynamic subarray configuration. The greedy algorithm can select the best subarrays from all the possible candidates in each search process, while the lanczos algorithm is applied to further reduce the computation complexity. Simulation results demonstrate the superior performance of the proposed algorithm to existing works yet with a lower complexity.

关键词： Massive MIMO mmWave communications hybrid precoding dynamic subarrays lanczos algorithm

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Fast Principal Component Auto-Regressive algorithm for Estimation of Parameters of Radar Interference Signal 10

Fast Principal Component Auto-Regressive Algorithm for Estim...

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10th International Conference on Computing, Communication and Networking Technologies (ICCCNT)

作者： Hussain, Md. Shahnawaz Pal, Srikanta Birla Inst Technol ECE Dept Ranchi Bihar India

ISBN: (纸本)9781538659069

The issue of estimation of parameters of radar interference signal has been addressed by algorithms like Grid Search-Maximum Likelihood Estimator (GS-MLE) and Principal Component Auto-Regressive Estimator (PCAR). GS-MLE algorithm is an optimal algorithm as it achieves the Cramer-Rao Lower Bound (CRLB) but its time-complexity is high. Another algorithm, that is, the PCAR algorithm is a suboptimal algorithm but it is comparatively faster. In this paper, we propose a hybrid method to further reduce the time-complexity of the PCAR algorithm for large data size (>3000) at both high SNR (>0 dB) and low SNR (<0 dB). However, the estimates of parameters obtained by the Fast PCAR algorithm are reliable only in the SNR range of -20 dB to infinity. This is validated by comparing the Fast PCAR algorithm with the CRLB.

关键词： Principal Component AR algorithm Grid Search Maximum Likelihood Estimator CRLB QR algorithm lanczos algorithm singular-value decomposition eigenvalues radar interference

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Random neural networks for dimensionality reduction and regularized supervised learning

Random neural networks for dimensionality reduction and regu...

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作者： Renjie Hu University of Iowa

学位级别：博士

This dissertation explores Random Neural Networks (RNNs) in several aspects and their applications. First, Novel RNNs have been proposed for dimensionality reduction and visualization. Based on Extreme Learning Machines (ELMs) and Self-Organizing Maps (SOMs) a new method is created to identify the important variables and visualize the data. This technique reduces the curse of dimensionality and improves furthermore the interpretability of the visualization and is tested on real nursing survey datasets. ELM-SOM+ is an autoencoder created to preserves the intrinsic quality of SOM and also brings continuity to the projection using two ELMs. This new methodology shows considerable improvement over SOM on real datasets. Second, as a Supervised Learning method, ELMs has been applied to the hierarchical multiscale method to bridge the the molecular dynamics to continua. The method is tested on simulation data and proven to be efficient for passing the information from one scale to another. Lastly, the regularization of ELMs has been studied and a new regularization algorithm for ELMs is created using a modified lanczos algorithm. The lanczos ELM on average divide computational time by 20 and reduce the Normalized MSE by 14% comparing with regular ELMs.

关键词： Data Visualization Dimensionality Reduction Feature Selection lanczos algorithm Random Neural Networks Regularization

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Block Krylov methods for accelerating ensembles of variational data assimilations

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QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY 2018年第717期144卷 2463-2480页

作者： Mercier, Francois Gurol, Selime Jolivet, Pierre Michel, Yann Montmerle, Thibaut Meteo France CNRS CNRM 42 Ave Gustave Coriolis F-31057 Toulouse France CERFACS Toulouse France CNRS IRIT Toulouse France

We consider the problem of efficiently solving ensembles of variational data assimilations in the context of numerical weather prediction. Running several assimilations notably allows us to initialize ensemble prediction systems and to more accurately represent background-error statistics, but is computationally expensive, limiting ensemble size. We propose a new class of algorithms for speeding up the minimization of the ensemble of data assimilations. It consists of using block Krylov methods to simultaneously perform the minimization for all members of the ensemble, instead of performing each minimization separately. We develop preconditioned block Krylov versions of the Full Orthogonal Method and of the lanczos algorithm in both primal and dual space. The latter works in observation space that is usually of smaller dimension than the state space, thus giving an advantage in terms of memory requirements and computational cost. We describe and compare several parallelization strategies for speeding up the minimization and limiting the communications. These methods have been tested on a quasi-geostrophic system, consisting of a simplified atmospheric circulation model equipped with an ensemble of 3D-Var schemes tuned to mimic some features of a limited-area numerical weather prediction system. Experimentation shows that the number of iterations needed to converge is drastically reduced by the block Krylov approaches. We indicate that, while working in primal space does not save significant computational time, working in the dual space may reduce the computational time by a factor of 2 to 5 (depending on ensemble size) compared to standard Krylov methods, making our approach attractive for operational use.

关键词： block Krylov techniques dual approach ensemble assimilation lanczos algorithm parallelism quasi-geostrophic model variational assimilation

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Conjugate Gradient algorithm in the Four-Dimensional Variational Data Assimilation System in GRAPES

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Journal of Meteorological Research 2018年第6期32卷 974-984页

作者： Yongzhu LIU Lin ZHANG Zhihua LIAN National Meteorological Center Beijing 100081

Minimization algorithms are singular components in four-dimensional variational data assimilation(4DVar).In this paper,the convergence and application of the conjugate gradient algorithm(CGA),which is based on the lanczos iterative algorithm and the Hessian matrix derived from tangent linear and adjoint models using a non-hydrostatic framework,are investigated in the 4DVar ***,the influence of the Gram-Schmidt orthogonalization of the lanczos vector on the convergence of the lanczos algorithm is *** results show that the lanczos algorithm without orthogonalization fails to converge after the ninth iteration in the 4DVar minimization,while the orthogonalized lanczos algorithm converges ***,the convergence and computational efficiency of the CGA and quasi-Newton method in batch cycling assimilation experiments are compared on the 4DVar platform of the Global/Regional Assimilation and Prediction System(GRAPES).The CGA is 40%more computationally efficient than the quasi-Newton method,although the equivalent analysis results can be obtained by using either the CGA or the quasi-Newton ***,the CGA based on lanczos iterations is better for solving the optimization problems in the GRAPES 4DVar system.

关键词： numerical weather prediction Global/Regional Assimilation and Prediction System four-dimensional variation conjugate gradient algorithm lanczos algorithm

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Modeling of first-order photobleaching kinetics using Krylov subspace spectral methods

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2018年第6期75卷 2153-2172页

作者： Sheikholeslami, Somayyeh Lambers, James V. Univ Southern Mississippi Dept Phys & Astron Hattiesburg MS 39406 USA Univ Southern Mississippi Dept Math Hattiesburg MS 39406 USA

We solve the first order 2-D reaction-diffusion equations which describe binding-diffusion kinetics using the photobleaching scanning profile of a confocal laser scanning microscope, approximated by a Gaussian laser profile. We show how to solve the first-order photobleaching kinetics partial differential equations (PDEs) using a time-stepping method known as a Krylov subspace spectral (KSS) method. KSS methods are explicit methods for solving time-dependent variable-coefficient partial differential equations. They approximate Fourier coefficients of the solution using Gaussian quadrature rules in the spectral domain. In this paper, we show how a KSS method can be used to obtain not only an approximate numerical solution, but also an approximate analytical solution when using initial conditions that come from pre-bleach steady states and also general initial conditions, to facilitate asymptotic analysis. Analytical and numerical results are presented. It is observed that although KSS methods are explicit, it is possible to use a time step that is far greater than what the CFL condition would indicate. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： lanczos algorithm Spectral methods Gaussian quadrature FRAP Photobleaching kinetics equation

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