This brief briefly addresses the problem of power flow solution for direct-current (dc) networks with radial configuration and constant power loads (CPLs). It proposes a novel iterative method based on the upper trian...
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This brief briefly addresses the problem of power flow solution for direct-current (dc) networks with radial configuration and constant power loads (CPLs). It proposes a novel iterative method based on the upper triangular relationship between nodal and branch currents, it also uses a primitive impedance matrix. The main advantage of this method lies in the possibility of avoiding inversions of non-diagonal matrices, which allows its convergence to be improved in terms of the number of iterations and processing times required in comparison to classical admittance-based methods. Three different radial dc resistive networks composed by 21, 33, and 69 nodes are employed to validate the effectiveness of the proposed power flow solution method. For comparison purposes, the Newton-Raphson method, and also successive approximations and Taylor-based approaches are implemented. All simulations have performed in MATLAB software.
In this paper, we establish a summability factor theorem for summability |A, delta|(k). This paper is an extension of the main result of Savas, E. A study on absolute summability factors for a triangular matrix. Math....
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In this paper, we establish a summability factor theorem for summability |A, delta|(k). This paper is an extension of the main result of Savas, E. A study on absolute summability factors for a triangular matrix. Math. Ineq. Appl., 2009, 12(19), 141-146.
We consider the problem of storing a triangular matrix so that each row and column is stored as a "vector," i.e., the locations form an arithmetic progression. Storing rows and columns as vectors can speed u...
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We consider the problem of storing a triangular matrix so that each row and column is stored as a "vector," i.e., the locations form an arithmetic progression. Storing rows and columns as vectors can speed up access significantly. We show that there is no such storage method that does not waste approximately one half of the computer memory.
Due to the robustness, the matrix inversion methods based on matrix factorization are often adopted in engineering while the triangular matrix inversion is one key part of those methods. This brief reviews the adjoint...
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Due to the robustness, the matrix inversion methods based on matrix factorization are often adopted in engineering while the triangular matrix inversion is one key part of those methods. This brief reviews the adjoint matrix and presents a novel scheme for field-programmable gate arrays (FPGAs) calculating the triangular matrix inversion. Employing the more characteristics of both the triangular matrix and its inversion, the proposed diagonal-wise algorithm for the triangular matrix inversion has the high parallelism and extensibility in the hardware implementation and is suitable for the different matrixtriangular factorization (QR, LDL, Cholesky and LU). Meanwhile, the recursive diagonal-wise algorithm is designed for the large scale triangular matrices. Compared with the traditional row-/column-wise methods, our algorithm has a good performance at the low computation load. Finally, the experiments are conducted on one Xilinx Virtex-7 FPGA to illustrate the performances of the four different methods.
In this article we consider the elements in upper triangular finite and infinite dimensional matrix groups over fields, whose order is equal to k (k is an element of N). For the case when the characteristic of K does ...
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In this article we consider the elements in upper triangular finite and infinite dimensional matrix groups over fields, whose order is equal to k (k is an element of N). For the case when the characteristic of K does not divide k, we give a description of such elements. Next using this criterion, we show how to find the number of these elements in finite dimensional groups when K is a finite field.
Broadband filtering and reconstruction-based spectral measurement represent a hot technical route for miniaturized spectral measurement;the measurement encoding scheme has a great effect on the spectral reconstruction...
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Broadband filtering and reconstruction-based spectral measurement represent a hot technical route for miniaturized spectral measurement;the measurement encoding scheme has a great effect on the spectral reconstruction fidelity. The existing spectral encoding schemes are usually complex and hard to implement;thus, the applications are severely limited. Considering this, here, a simple spectral encoding method based on a triangular matrix is designed. The condition number of the proposed spectral encoding system is estimated and demonstrated to be relatively low theoretically;then, verification experiments are carried out, and the results show that the proposed encoding can work well under precise or unprecise encoding and measurement conditions;therefore, the proposed scheme is demonstrated to be an effective trade-off of the spectral encoding efficiency and implementation cost.
The area of matrix functions has received growing interest for a long period of time due to their growing applications. Having a numerical algorithm for a matrix function, the ideal situation is to have an estimate or...
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The area of matrix functions has received growing interest for a long period of time due to their growing applications. Having a numerical algorithm for a matrix function, the ideal situation is to have an estimate or bound for the error returned alongside the solution. Condition numbers serve this purpose;they measure the first -order sensitivity of matrix functions to perturbations in the input data. We have observed that the existing unstructured condition number leads most of the time to inferior bounds of relative forward errors for some matrix functions at triangular and quasi -triangular matrices. We propose a condition number of matrix functions exploiting the structure of triangular and quasi -triangular matrices. We then adapt an existing algorithm for exact computation of the unstructured condition number to an algorithm for exact evaluation of the structured condition number. Although these algorithms are direct rather than iterative and useful for testing the numerical stability of numerical algorithms, they are less practical for relatively large problems. Therefore, we use an implicit power method approach to estimate the structured condition number. Our numerical experiments show that the structured condition number captures the behavior of the numerical algorithms and provides sharp bounds for the relative forward errors. In addition, the experiment indicates that the power method algorithm is reliable to estimate the structured condition number.
Let H be a subgroup of the symmetric group S-n and chi an irreducible character of H. In this paper we give conditions that characterize matrices that leave invariant the value of a given generalized matrix function o...
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Let H be a subgroup of the symmetric group S-n and chi an irreducible character of H. In this paper we give conditions that characterize matrices that leave invariant the value of a given generalized matrix function on the set of upper triangular matrices. In some cases we describe completely these matrices. (c) 2003 Elsevier Inc. All rights reserved.
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