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Energy and AI 2023年第4期14卷 17-30页

作者： dax k.matthews University of Hawaii at Manoa Hawaii Natural Energy Institute(HNEI)1680 East West RoadPOST 109Honolulu96822HIUSA

Photovoltaic technologies provide significant capacity to electric grids,however,resource variability and production uncertainty complicate power balancing and reserve management.A crucial step in predicting solar generation is determining clear-sky ***-sky attenuation can be modeled using broadband atmospheric turbidity factors,but model accuracy is dependent on the measurements used to determine the current and future state of aerosol loading and water vapor content,which requires close proximity measurements,in time and space,to account for turbidity *** measurements,though,are only available in near real-time at a limited,and decreasing,number of *** paper proposes a new method for estimating time-varying local turbidity conditions from more readily available pyranometer or PV output *** method employs a long short-term memory recurrent neural network to distill the turbidity-driven signal from global irradiance(or global irradiance driven)observations,despite an inherent dampening *** method is developed to operate in near real-time for solar forecasting *** examines the ability of the method to(1)reproduce turbidity estimates derived from historical measurements of beam irradiance under clear-sky conditions;and(2)provide input for clear-sky models in the form of persistence forecasts generated from daily mean values.

关键词： Solar power forecasting Broadband atmospheric turbidity Clear-sky modeling

A Compact Heart Iteration for Large Eigenvalues Problems

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Advances in Linear Algebra & Matrix Theory 2022年第1期12卷 24-38页

作者： Achiya dax Hydrological Service of Israel Jerusalem Israel

In this paper, we present a compact version of the Heart iteration. One that requires less matrix-vector products per iteration and attains faster convergence. The Heart iteration is a new type of Restarted krylov methods for calculating peripheral eigenvalues of symmetric matrices. The new framework avoids the Lanczos tridiagonalization process and the use of implicit restarts. This simplifies the restarting mechanism and allows the introduction of several modifications. Convergence is assured by a monotonicity property that pushes the computed Ritz values toward their limits. Numerical experiments illustrate the usefulness of the proposed approach.

关键词： Large Sparse Matrices Restarted krylov Methods Exterior Eigenvalues Symmetric Matrices Monotonicity Starting Vectors

The Equivalence between Orthogonal Iterations and Alternating Least Squares

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Advances in Linear Algebra & Matrix Theory 2020年第2期10卷 7-21页

作者： Achiya dax Hydrological Service Jerusalem Israel

This note explores the relations between two different methods. The first one is the Alternating Least Squares (ALS) method for calculating a rank-k approximation of a real m×n matrix, A. This method has important applications in nonnegative matrix factorizations, in matrix completion problems, and in tensor approximations. The second method is called Orthogonal Iterations. Other names of this method are Subspace Iterations, Simultaneous Iterations, and block-Power method. Given a real symmetric matrix, G, this method computes k dominant eigenvectors of G. To see the relation between these methods we assume that G = AT A. It is shown that in this case the two methods generate the same sequence of subspaces, and the same sequence of low-rank approximations. This equivalence provides new insight into the convergence properties of both methods.

关键词： Alternating Least Squares (ALS) Orthogonal Iterations Equivalence Relations Low-Rank Approximations

A Subspace Iteration for Calculating a Cluster of Exterior Eigenvalues

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Advances in Linear Algebra & Matrix Theory 2015年第3期5卷 76-89页

作者： Achiya dax Hydrological Service Jerusalem Israel

In this paper we present a new subspace iteration for calculating eigenvalues of symmetric matrices. The method is designed to compute a cluster of k exterior eigenvalues. For example, k eigenvalues with the largest absolute values, the k algebraically largest eigenvalues, or the k algebraically smallest eigenvalues. The new iteration applies a Restarted krylov method to collect information on the desired cluster. It is shown that the estimated eigenvalues proceed monotonically toward their limits. Another innovation regards the choice of starting points for the krylov subspaces, which leads to fast rate of convergence. Numerical experiments illustrate the viability of the proposed ideas.

关键词： Exterior Eigenvalues Symmetric Matrices Subspace Iterations Interlacing Restarted krylov Methods

Maximum Principles for Normal Matrices

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Advances in Linear Algebra & Matrix Theory 2019年第3期9卷 73-81页

作者： Achiya dax Hydrological Service Jerusalem Israel

ky Fan maximum principle is a well-known observation about traces of certain hermitian matrices. In this note, we derive a powerful extension of this claim. The extension is achieved in three ways. First, traces are replaced with norms of diagonal matrices, and any unitarily invariant norm can be used. Second, hermitian matrices are replaced by normal matrices, so the rule applies to a larger class of matrices. Third, diagonal entries can be replaced with eigenvalues and singular values. It is shown that the new maximum principle is closely related to the problem of approximating one matrix by another matrix of a lower rank.

关键词： ky Fan Maximum Principle Normal Matrices Extended Maximum Principle Unitarily Invariant Norms

Low-Rank Positive Approximants of Symmetric Matrices

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Advances in Linear Algebra & Matrix Theory 2014年第3期4卷 172-185页

作者： Achiya dax Hydrological Service Jerusalem Israel

Given a symmetric matrix X, we consider the problem of finding a low-rank positive approximant of X. That is, a symmetric positive semidefinite matrix, S, whose rank is smaller than a given positive integer, , which is nearest to X in a certain matrix norm. The problem is first solved with regard to four common norms: The Frobenius norm, the Schatten p-norm, the trace norm, and the spectral norm. Then the solution is extended to any unitarily invariant matrix norm. The proof is based on a subtle combination of ky Fan dominance theorem, a modified pinching principle, and Mirsky minimum-norm theorem.

关键词： Low-Rank Positive Approximants Unitarily Invariant Matrix Norms

From Eigenvalues to Singular Values: A Review

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Advances in Pure Mathematics 2013年第9期3卷 8-24页

作者： Achiya dax Hydrological Service Jerusalem Israel

The analogy between eigenvalues and singular values has many faces. The current review brings together several examples of this analogy. One example regards the similarity between Symmetric Rayleigh Quotients and Rectangular Rayleigh Quotients. Many useful properties of eigenvalues stem are from the Courant-Fischer minimax theorem, from Weyl’s theorem, and their corollaries. Another aspect regards “rectangular” versions of these theorems. Comparing the properties of Rayleigh Quotient matrices with those of Orthogonal Quotient matrices illuminates the subject in a new light. The Orthogonal Quotients Equality is a recent result that converts Eckart-Young’s minimum norm problem into an equivalent maximum norm problem. This exposes a surprising link between the Eckart-Young theorem and ky Fan’s maximum principle. We see that the two theorems reflect two sides of the same coin: there exists a more general maximum principle from which both theorems are easily derived. ky Fan has used his extremum principle (on traces of matrices) to derive analog results on determinants of positive definite Rayleigh Quotients matrices. The new extremum principle extends these results to Rectangular Quotients matrices. Bringing all these topics under one roof provides new insight into the fascinating relations between eigenvalues and singular values.

关键词： Eigenvalues Singular Values Rayleigh Quotient Orthogonal Quotient Matrices The Orthogonal Quotients Equality Eckart-Young Theorem ky Fan’s Extremum Principles

A New Type of Restarted krylov Methods

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Advances in Linear Algebra & Matrix Theory 2017年第1期7卷 18-28页

作者： Achiya dax Hydrological Service Jerusalem Israel

In this paper we present a new type of Restarted krylov methods for calculating peripheral eigenvalues of symmetric matrices. The new framework avoids the Lanczos tridiagonalization process, and the use of polynomial filtering. This simplifies the restarting mechanism and allows the introduction of several modifications. Convergence is assured by a monotonicity property that pushes the eigenvalues toward their limits. The krylov matrices that we use lead to fast rate of convergence. Numerical experiments illustrate the usefulness of the proposed approach.

关键词： Restarted krylov Methods Exterior Eigenvalues Symmetric Matrices Monotonicity Starting Vectors

Bounding Inequalities for Eigenvalues of Principal Submatrices

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Advances in Linear Algebra & Matrix Theory 2019年第2期9卷 21-34页

作者： Achiya dax Hydrological Service Jerusalem Israel

ky Fan trace theorems and the interlacing theorems of Cauchy and Poincaré are important observations that characterize Hermitian matrices. In this note, we introduce a new type of inequalities which extend these theorems. The new inequalities are obtained from the old ones by replacing eigenvalues and diagonal entries with their moduli. This modification yields effective bounding inequalities which are valid on a larger range of matrices.

关键词： Cauchy Interlacing Theorem Poincaré Interlacing Theorem ky Fan Trace Theorems Non-Hermitian Matrices Normal Matrices Bounding Inequalities

Applicability limits of the dax test in plastic bonded explosives

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Defence Technology（防务技术） 2024年第6期36卷 64-70页

作者： Martin künzel Jindrich kucera Jiri Pachman OZM Research Bliznovice 32Hrochuv Tynec 53862Czech Republic Institute of Energetic Materials Faculty of Chemical TechnologyUniversity of PardubiceStudentska 95Pardubice 53210Czech Republic

The Disc Acceleration e Xperiment(dax)is one of the most recent experimental methods of performance characterization of new energetic materials.A cylindrical explosive charge accelerates a thin metallic disc and its velocity is measured continuously using photonic Doppler *** detonation velocity is measured *** dax test can be used to obtain the Chapman-Jouguet(CJ)detonation pressure and to describe detonation products expansion using reduced amount of explosive.A series of dax tests was performed at various charge diameters and disc thicknesses with Semtex 1 A plastic bonded explosive and sensitized *** dax-like evaluation was also applied to previously measured data of Semtex 1A and A-IX-1 *** optimum disc thickness is determined by the disc to explosive mass ratio of *** repeatability of the Semtex 1 A detonation pressure results is about four times lower compared to the pressed and liquid explosives.

关键词： Flyer plate Detonation pressure Photonic Doppler velocimetry Semtex