Relevant bibliographies by topics / Matrix Polynomial Problem

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Academic literature on the topic 'Matrix Polynomial Problem'

Author: Grafiati
Published: 4 June 2021
Last updated: 15 February 2022

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Journal articles on the topic "Matrix Polynomial Problem"

1

Das, Biswajit, and Shreemayee Bora. "Vector Spaces of Generalized Linearizations for Rectangular Matrix Polynomials." Electronic Journal of Linear Algebra 35 (February 1, 2019): 116–55. http://dx.doi.org/10.13001/1081-3810.3845.

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The complete eigenvalue problem associated with a rectangular matrix polynomial is typically solved via the technique of linearization. This work introduces the concept of generalized linearizations of rectangular matrix polynomials. For a given rectangular matrix polynomial, it also proposes vector spaces of rectangular matrix pencils with the property that almost every pencil is a generalized linearization of the matrix polynomial which can then be used to solve the complete eigenvalue problem associated with the polynomial. The properties of these vector spaces are similar to those introduc
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2

陈, 贺. "Two Solutions of Matrix Polynomial Problem." Pure Mathematics 11, no. 02 (2021): 310–12. http://dx.doi.org/10.12677/pm.2021.112040.

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3

Dey, Papri. "Definite determinantal representations of multivariate polynomials." Journal of Algebra and Its Applications 19, no. 07 (2019): 2050129. http://dx.doi.org/10.1142/s0219498820501297.

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In this paper, we consider the problem of representing a multivariate polynomial as the determinant of a definite (monic) symmetric/Hermitian linear matrix polynomial (LMP). Such a polynomial is known as determinantal polynomial. Determinantal polynomials can characterize the feasible sets of semidefinite programming (SDP) problems that motivates us to deal with this problem. We introduce the notion of generalized mixed discriminant (GMD) of matrices which translates the determinantal representation problem into computing a point of a real variety of a specified ideal. We develop an algorithm
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4

Buyukkoroglu, Taner, Gokhan Celebi, and Vakif Dzhafarov. "On the Robust Stability of Polynomial Matrix Families." Electronic Journal of Linear Algebra 30 (February 8, 2015): 905–15. http://dx.doi.org/10.13001/1081-3810.3093.

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In this study, the problem of robust asymptotic stability of n by n polynomial matrix family, in both continuous-time and discrete-time cases, is considered. It is shown that in the continuous case the problem can be reduced to positivity of two specially constructed multivariable polynomials, whereas in the discrete-time case it is required three polynomials. A number of examples are given, where the Bernstein expansion method and sufficient conditions from [L.H. Keel and S.P. Bhattacharya. Robust stability via sign-definite decomposition. IEEE Transactions on Automatic Control, 56(1):140–1
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5

Tansuwannont, Theerapat, Surachate Limkumnerd, Sujin Suwanna, and Pruet Kalasuwan. "Quantum Phase Estimation Algorithm for Finding Polynomial Roots." Open Physics 17, no. 1 (2019): 839–49. http://dx.doi.org/10.1515/phys-2019-0087.

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AbstractQuantum algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a quantum algorithm for finding the roots of nth degree polynomials where n is any positive integer. In classical algorithm, the resources required for solving this problem increase drastically when n increases and it would be impossible to practically solve the problem when n is large. It was found that any polynomial can be rearranged into a corresponding co
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6

Sharma, Bhuvnesh, Sunil Kumar, M. K. Paswan, and Dindayal Mahato. "Chebyshev Operational Matrix Method for Lane-Emden Problem." Nonlinear Engineering 8, no. 1 (2019): 1–9. http://dx.doi.org/10.1515/nleng-2017-0157.

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AbstractIn the this paper, a new modified method is proposed for solving linear and nonlinear Lane-Emden type equations using first kind Chebyshev operational matrix of differentiation. The properties of first kind Chebyshev polynomial and their shifted polynomial are first presented. These properties together with the operation matrix of differentiation of first kind Chebyshev polynomial are utilized to obtain numerical solutions of a class of linear and nonlinear LaneEmden type singular initial value problems (IVPs). The absolute error of this method is graphically presented. The proposed fr
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7

Grigoriu, Mircea. "Eigenvalue Problem for Uncertain Systems." Applied Mechanics Reviews 44, no. 11S (1991): S89—S95. http://dx.doi.org/10.1115/1.3121377.

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Methods are developed for calculating probabilistic characteristics of the eigenvalues of stochastic symmetric matrices. The methods are based on the relationship between the elements of a matrix and its eigenvalues, perturbation method, bounds on eigenvalues, and zero-crossings of the characteristic polynomial. It is shown that the polynomial characteristic of a stochastic matrix can be viewed as a random process whose crossings of level zero define the eigenvalues of the matrix. The proposed methods of analysis are demonstrated by examples from dynamics and elasticity.
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8

GRIMBLE, M. J. "Polynomial matrix solution to the standardH2optimal control problem." International Journal of Systems Science 22, no. 5 (1991): 793–806. http://dx.doi.org/10.1080/00207729108910661.

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9

Djidjev, Hristo N., Georg Hahn, Susan M. Mniszewski, Christian F. A. Negre, and Anders M. N. Niklasson. "Using Graph Partitioning for Scalable Distributed Quantum Molecular Dynamics." Algorithms 12, no. 9 (2019): 187. http://dx.doi.org/10.3390/a12090187.

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The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several advanced algorithms relying on evaluations of matrix polynomials have been published in the literature for such simulations. We aim to use a special type of graph partitioning to efficiently parallelize these computations. For this, we create a graph representing the zero–nonzero structure of a thresholded density matrix, and partition that graph into several co
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10

HOANG, THANH MINH, and THOMAS THIERAUF. "ON THE MINIMAL POLYNOMIAL OF A MATRIX." International Journal of Foundations of Computer Science 15, no. 01 (2004): 89–105. http://dx.doi.org/10.1142/s0129054104002327.

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We investigate the complexity of the degree and the constant term of the minimal polynomial of a matrix. We show that the degree of the minimal polynomial is computationally equivalent to the matrix rank. We compare the constant term of the minimal polynomial with the constant term of the characteristic polynomial. The latter is known to be computable in the logspace counting class GapL. We show that if this holds for the minimal polynomial as well, then the exact counting in logspace class C=L is closed under complement. Whether C=L is closed under complement is one of the main open problems
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