Approximate greatest common divisor of several polynomials from Hankel matrices

2021 ◽  
Vol 55 (3) ◽  
pp. 77-81
Author(s):  
Skander Belhaj ◽  
Abdulrahman Alsulami
Keyword(s):  
Hankel Matrix ◽  
New Method ◽  
Greatest Common Divisor ◽  
Hankel Matrices

This paper is devoted to present a new method for computing the approximate Greatest Common Divisor (GCD) of several polynomials (not pairwise) from the generalized Hankel matrix. Our approach based on the calculation of cofactors is tested for several sets of polynomials.

scholarly journals On Determinantal Varieties of Hankel Matrices

Algebra ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Edoardo Ballico ◽  
Michele Elia
Keyword(s):  
Finite Field ◽  
Hankel Matrix ◽  
Hankel Matrices ◽  
Linear Forms ◽  
Determinantal Varieties

Let ℌ be a class of n×n Hankel matrices HA whose entries, depending on a given matrix A, are linear forms in n variables with coefficients in a finite field 𝔽q. For every matrix in ℌ, it is shown that the varieties specified by the leading minors of orders from 1 to n-1 have the same number qn-1 of points in 𝔽qn. Further properties are derived, which show that sets of varieties, tied to a given Hankel matrix, resemble a set of hyperplanes as regards the number of points of their intersections.

scholarly journals Orthogonal diagonalization for complex skew-persymmetric anti-tridiagonal Hankel matrices

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Jesús Gutiérrez-Gutiérrez ◽  
Marta Zárraga-Rodríguez
Keyword(s):  
Hankel Matrix ◽  
Eigenvalue Decomposition ◽  
Hankel Matrices

AbstractIn this paper, we obtain an eigenvalue decomposition for any complex skew-persymmetric anti-tridiagonal Hankel matrix where the eigenvector matrix is orthogonal.

The Explicit Inverses of CUPL-Toeplitz and CUPL-Hankel Matrices

2017 ◽  
Vol 7 (1) ◽  
pp. 38-54 ◽  
Author(s):  
Zhao-Lin Jiang ◽  
Xiao-Ting Chen ◽  
Jian-Min Wang
Keyword(s):  
Toeplitz Matrix ◽  
Hankel Matrix ◽  
Structured Matrices ◽  
Hankel Matrices ◽  
The Stability

AbstractIn this paper, we consider two innovative structured matrices, CUPL-Toeplitz matrix and CUPL-Hankel matrix. The inverses of CUPL-Toeplitz and CUPL-Hankel matrices can be expressed by the Gohberg-Heinig type formulas, and the stability of the inverse matrices is verified in terms of 1-, ∞- and 2-norms, respectively. In addition, two algorithms for the inverses of CUPL-Toeplitz and CUPL-Hankel matrices are given and examples are provided to verify the feasibility of these algorithms.

scholarly journals Companion matrices and their relations to Toeplitz and Hankel matrices

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Yousong Luo ◽  
Robin Hill
Keyword(s):  
Hankel Matrix ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Hankel Matrices ◽  
Hankel Structure ◽  
Companion Matrices ◽  
Necessary And Sufficient ◽  
Special Case

AbstractIn this paper we describe some properties of companion matrices and demonstrate some special patterns that arisewhen a Toeplitz or a Hankel matrix is multiplied by a related companion matrix.We present a necessary and sufficient condition, generalizing known results, for a matrix to be the transforming matrix for a similarity between a pair of companion matrices. A special case of our main result shows that a Toeplitz or a Hankel matrix can be extended using associated companion matrices, preserving the Toeplitz or Hankel structure respectively.

scholarly journals Low Density Parity Check Codes Constructed from Hankel Matrices

2018 ◽  
Vol 3 ◽  
pp. 37-41
Author(s):  
Mohammed Amine Tehami ◽  
Ali Djebbari
Keyword(s):  
Channel Coding ◽  
Additive White Gaussian Noise ◽  
Hankel Matrix ◽  
Low Density ◽  
Parity Check ◽  
Hankel Matrices ◽  
Permutation Matrices ◽  
Low Density Parity Check ◽  
The Matrix ◽  
Parity Check Codes

In this paper, a new technique for constructing low density parity check codes based on the Hankel matrix and circulant permutation matrices is proposed. The new codes are exempt of any cycle of length 4. To ensure that parity check bits can be recursively calculated with linear computational complexity, a dual-diagonal structure is applied to the parity check matrices of those codes. The proposed codes provide a very low encoding complexity and reduce the stored memory of the matrix H in which this matrix can be easily implemented comparing to others codes used in channel coding. The new LDPC codes are compared, by simulation, with uncoded bi-phase shift keying (BPSK). The result shows that the proposed codes perform very well over additive white Gaussian noise (AWGN) channels.

scholarly journals Some Propositions on Generalized Nevanlinna Functions of the ClassNk

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Yan-Ping Song ◽  
Hui-Feng Hao ◽  
Yong-Jian Hu ◽  
Gong-Ning Chen
Keyword(s):  
Asymptotic Expansion ◽  
Hankel Matrix ◽  
Real Point ◽  
Hankel Matrices ◽  
Nevanlinna Function ◽  
Generalized Nevanlinna Function ◽  
Uniform Asymptotic Expansion ◽  
Nevanlinna Functions ◽  
Definition Of ◽  
Inertia Index

Some propositions on the generalized Nevanlinna functions are derived. We indicate mainly that (1) the negative inertia index of a Hermitian generalized Loewner matrix generated by a generalized Nevanlinna function in the classNκdoes not exceedκ. This leads to an equivalent definition of a generalized Nevanlinna function; (2) if a generalized Nevanlinna function in the classNκhas a uniform asymptotic expansion at a real pointαor at infinity, then the negative inertia index of the Hankel matrix constructed with the partial coefficients of that asymptotic expansion does not exceedκ. Also, an explicit formula for the negative index of a real rational function is given by using relations among Loewner, Bézout, and Hankel matrices. These results will provide first tools for the solution of the indefinite truncated moment problems together with the multiple Nevanlinna-Pick interpolation problems in the classNκbased on the so-called Hankel vector approach.

Selective Sampling and Orientation of Non-Homogeneous Tissues

1968 ◽  
Vol 26 ◽  
pp. 98-99
Author(s):  
C. C. Clawson ◽  
L. W. Anderson ◽  
R. A. Good
Keyword(s):  
Electron Microscopy ◽  
Electron Microscope ◽  
Light Microscopy ◽  
Random Sampling ◽  
New Method ◽  
Microscope Examination ◽  
Small Areas ◽  
Selective Sampling ◽  
Large Numbers ◽  
Specific Orientation

Investigations which require electron microscope examination of a few specific areas of non-homogeneous tissues make random sampling of small blocks an inefficient and unrewarding procedure. Therefore, several investigators have devised methods which allow obtaining sample blocks for electron microscopy from region of tissue previously identified by light microscopy of present here techniques which make possible: 1) sampling tissue for electron microscopy from selected areas previously identified by light microscopy of relatively large pieces of tissue; 2) dehydration and embedding large numbers of individually identified blocks while keeping each one separate; 3) a new method of maintaining specific orientation of blocks during embedding; 4) special light microscopic staining or fluorescent procedures and electron microscopy on immediately adjacent small areas of tissue.

A new method for the determination of nitrates

1960 ◽  
Vol 23 ◽  
pp. 227-232 ◽  
Author(s):  
P WEST ◽  
G LYLES
Keyword(s):  
New Method
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