The aim of dimension reduction techniques is to eliminate unnecessary information from extensive datasets, thereby enhancing the effectiveness of data analysis. Some linear dimension reduction techniques can be formul...
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An iterative algorithm is presented for solving the RPA equations of linear response. The method optimally computes energy-weighted moments of the strength function, allowing one to match the computational effort to t...
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An iterative algorithm is presented for solving the RPA equations of linear response. The method optimally computes energy-weighted moments of the strength function, allowing one to match the computational effort to the intrinsic accuracy of the basic mean-field approximation, avoiding the problem of solving very large matrices. For local interactions, the computational effort for the method scales with the number of particles N-p as O(N-p(3)). (C) 1999 Elsevier Science B.V. All rights reserved.
A new method for computing transient electromagnetic wavefields in inhomogeneous and lossy media is presented. The method utilizes a modified lanczos scheme, where a so-called reduced model is constructed. A discretiz...
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A new method for computing transient electromagnetic wavefields in inhomogeneous and lossy media is presented. The method utilizes a modified lanczos scheme, where a so-called reduced model is constructed. A discretization of the time variable is then superfluous. This reduced model represents the transient electromagnetic wavefield on a certain bounded interval in time. Some theoretical aspects of the method are highlighted and numerical results showing the performance of the method for two-dimensional (2-D) configurations are given. Also, comparisons between this lanczos method and the finite-difference time-domain (FDTD) method are made.
The k-step explicit restart lanczos algorithm, LExpRes, for the computation of a few of the extreme eigenpairs of large, usually sparse, symmetric matrices, computes one eigenpair at a time using a deflation technique...
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The k-step explicit restart lanczos algorithm, LExpRes, for the computation of a few of the extreme eigenpairs of large, usually sparse, symmetric matrices, computes one eigenpair at a time using a deflation technique in which each lanczos vector generated is orthogonalized against all previously converged eigenvectors. The computation of the inner products associated with this external orthogonalization often creates a bottleneck in parallel distributed memory environments. In this paper methods are proposed which significantly reduce this computational overhead in LExpRes, thereby effectively improving its efficiency. The performances of these methods on the Cray-T3D and the Cray-T3E are assessed and critically compared with that of the original algorithm. (C) 2001 Elsevier Science B.V. All rights reserved.
This paper presents a new regularization for Extreme Learning Machines (ELMs). ELMs are Randomized Neural Networks (RNNs) that are known for their fast training speed and good accuracy. Nevertheless the complexity of ...
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This paper presents a new regularization for Extreme Learning Machines (ELMs). ELMs are Randomized Neural Networks (RNNs) that are known for their fast training speed and good accuracy. Nevertheless the complexity of ELMs has to be selected, and regularization has to be performed in order to avoid under-fitting or overfitting. Therefore, a novel Regularization is proposed using a modified lanczos algorithm: Iterative lanczos Extreme Learning Machine (Lan-ELM). As summarized in the experimental Section, the computational time is on average divided by 4 and the Normalized MSE is on average reduced by 11%. In addition, the proposed method can be intuitively parallelized, which makes it a very valuable tool to analyze huge data sets in real-time. (C) 2020 Elsevier B.V. All rights reserved.
In this paper, the computation of the smallest eigenvalues and the corresponding eigenvectors of the generalized eigenvalue problem using lanczos algorithm with a recursive partitioning method as well as the Sturm seq...
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In this paper, the computation of the smallest eigenvalues and the corresponding eigenvectors of the generalized eigenvalue problem using lanczos algorithm with a recursive partitioning method as well as the Sturm sequence-bisection method have been discussed. We have also presented the comparison of the numerical results and the CPU-time between the above two methodologies. Our comparative study indicates that the lanczos with a recursive partitioning method takes relatively less computing time than that of the Sturm sequence-bisection method. (C) 2000 Elsevier Science Ltd. All rights reserved.
lanczos vectors computed in finite precision arithmetic by the three-term recurrence tend to lose their mutual biorthogonality One either accepts this loss and takes more steps or re-biorthogonalizes the lanczos vecto...
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lanczos vectors computed in finite precision arithmetic by the three-term recurrence tend to lose their mutual biorthogonality One either accepts this loss and takes more steps or re-biorthogonalizes the lanczos vectors at each step. Far the symmetric case, there is a compromise approach. This compromise, known as maintaining semiorthogonality, minimizes the cost of reorthogonalization. This paper extends the compromise to the true-sided lanczos algorithm and justifies the new algorithm. The compromise is called maintaining semiduality. An advantage of maintaining semiduality is that the computed tridiagonal is a perturbation of a matrix that is exactly similar to the appropriate projection of the given matrix onto the computed subspaces. Another benefit is that the simple two-sided Gram-Schmidt procedure is a viable way to correct for loss of duality. A numerical experiment is included in which our lanczos code is significantly more efficient than Arnoldi's method.
We study the lanczos algorithm where the initial vector is sampled uniformly from Sn-1. Let A be an n x n Hermitian matrix. We show that when run for few iterations, the output of lanczos on A is almost deterministic....
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We study the lanczos algorithm where the initial vector is sampled uniformly from Sn-1. Let A be an n x n Hermitian matrix. We show that when run for few iterations, the output of lanczos on A is almost deterministic. More precisely, we show that for any epsilon is an element of (0, 1) there exists c > 0 depending only on epsilon and a certain global property of the spectrum of A (in particular, not depending on n) such that when lanczos is run for at most c log n iterations, the output Jacobi coefficients deviate from their medians by t with probability at most exp(-n(epsilon) t(2)) for t < parallel to A parallel to. We directly obtain a similar result for the Ritz values and vectors. Our techniques also yield asymptotic results: Suppose one runs lanczos on a sequence of Hermitian matrices A(n) is an element of M-n(C) whose spectral distributions converge in Kolmogorov distance with rate O(n(-epsilon)) to a density mu for some epsilon > 0. Then we show that for large enough n, and for k = O(root log n), the Jacobi coefficients output after k iterations concentrate around those for mu. The asymptotic setting is relevant since lanczos is often used to approximate the spectral density of an infinite-dimensional operator by way of the Jacobi coefficients;our result provides some theoretical justification for this approach. In a different direction, we show that lanczos fails with high probability to identify outliers of the spectrum when run for at most c' log n iterations, where again c' depends only on the same global property of the spectrum of A. Classical results imply that the bound c' log n is tight up to a constant factor.
This paper tries to accelerate the convergence rate of the general viscous dynamic relaxation method. For this purpose, a new automated procedure for estimating the critical damping factor is developed by employing a ...
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This paper tries to accelerate the convergence rate of the general viscous dynamic relaxation method. For this purpose, a new automated procedure for estimating the critical damping factor is developed by employing a simple variant of the lanczos algorithm, which does not require any re-orthogonalization process. All of the computational operations are performed by simple vector-matrix multiplication without requiring any matrix factorization or inversion. Some numerical examples with geometric nonlinear behavior are analyzed by the proposed algorithm. Results show that the suggested procedure could effectively decrease the total number of convergence iterations compared with the conventional dynamic relaxation algorithms. Copyright (C) 2017 John Wiley & Sons, Ltd.
The lanczos algorithm with a new recursive partitioning method to compute the eigenvalues, in a given specified interval, is presented in this paper. Comparisons have been made respecting the numerical results as well...
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The lanczos algorithm with a new recursive partitioning method to compute the eigenvalues, in a given specified interval, is presented in this paper. Comparisons have been made respecting the numerical results as well as the CPU-time with that of the Sturm sequence-bisection method. (C) 1999 Elsevier Science Ltd. All rights reserved.
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