Diagonalization and spectral decomposition of factor block circulant matrices

Claeyssen, Julio Cesar Ruiz; Leal, Liara Aparecida dos Santos

doi:10.1016/0024-3795(88)90124-3

Cited by 22 publications

(8 citation statements)

References 3 publications

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“…Using the terminology of [69],ĉ yκ (z) is a z-factor block circulant matrix of type (y, 2κ). The spectrum σ[ĉ yκ (z)] ofĉ yκ (z) is easily obtained, and is given by…”

Section: Discussionmentioning

confidence: 99%

Charges and currents in quantum spin chains: late-time dynamics and spontaneous currents

Fagotti¹

2016

J. Phys. A: Math. Theor.

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We review the structure of the conservation laws in noninteracting spin chains and unveil a formal expression for the corresponding currents. We briefly discuss how interactions affect the picture. In the second part, we explore the effects of a localized defect. We show that the emergence of spontaneous currents near the defect undermines any description of the late-time dynamics by means of a stationary state in a finite chain. In particular, the diagonal ensemble does not work. Finally, we provide numerical evidence that simple generic localized defects are not sufficient to induce thermalization.

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“…Using the terminology of [69],ĉ yκ (z) is a z-factor block circulant matrix of type (y, 2κ). The spectrum σ[ĉ yκ (z)] ofĉ yκ (z) is easily obtained, and is given by…”

Section: Discussionmentioning

confidence: 99%

Charges and currents in quantum spin chains: late-time dynamics and spontaneous currents

Fagotti¹

2016

J. Phys. A: Math. Theor.

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“…In [6], Jin et al proposed the GMRES method with the Strangtype block-circulant preconditioner for solving singular perturbation delay differential equations. In [7], Claeyssen and Leal introduce factor circulant matrices: matrices with the structure of circulants, but with the entries below the diagonal multiplied by the same factor. The diagonalization of a circulant matrix and spectral decomposition are conveniently generalized to block matrices with the structure of factor circulants.…”

Section: Introductionmentioning

confidence: 99%

On the Minimal Polynomials and the Inverses of Multilevel Scaled Factor Circulant Matrices

Jiang

2014

Abstract and Applied Analysis

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Circulant matrices have important applications in solving various differential equations. The level-kscaled factor circulant matrix over any field is introduced. Algorithms for finding the minimal polynomial of this kind of matrices over any field are presented by means of the algorithm for the Gröbner basis of the ideal in the polynomial ring. And two algorithms for finding the inverses of such matrices are also presented. Finally, an algorithm for computing the inverse of partitioned matrix with level-kscaled factor circulant matrix blocks over any field is given by using the Schur complement, which can be realized by CoCoA 4.0, an algebraic system, over the field of rational numbers or the field of residue classes of modulo prime number.

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“…Circulant matrices arise in many applications in mathematics, physics, and other applied sciences in problems possessing a periodicity property [12][13][14][15][16][17][18][19] and they have been put on a firm basis with the work of Davis [20] and Jiang and Zhou [21]. The circulant matrices, long a fruitful subject of research [20,21], have in recent years been extended in many directions [22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

“…The circulant matrices, long a fruitful subject of research [20,21], have in recent years been extended in many directions [22][23][24][25][26]. Factor block circulant matrices and − − 1-circulants are other natural extensions of this wellstudied class and can be found in [12,13].…”

Section: Introductionmentioning

confidence: 99%

Fast Algorithms for Solving FLSR-Factor Block Circulant Linear Systems and Inverse Problem ofAX=b

Jiang

2014

Abstract and Applied Analysis

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Block circulant and circulant matrices have already become an ideal research area for solving various differential equations. In this paper, we give the definition and the basic properties of FLSR-factor block circulant (retrocirculant) matrix over fieldF. Fast algorithms for solving systems of linear equations involving these matrices are presented by the fast algorithm for computing matrix polynomials. The unique solution is obtained when such matrix over a fieldFis nonsingular. Fast algorithms for solving the unique solution of the inverse problem ofAX=bin the class of the level-2 FLS(R,r)-circulant(retrocirculant) matrix of type(m,n)over fieldFare given by the right largest common factor of the matrix polynomial. Numerical examples show the effectiveness of the algorithms.

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Diagonalization and spectral decomposition of factor block circulant matrices

Cited by 22 publications

References 3 publications

Charges and currents in quantum spin chains: late-time dynamics and spontaneous currents

Charges and currents in quantum spin chains: late-time dynamics and spontaneous currents

On the Minimal Polynomials and the Inverses of Multilevel Scaled Factor Circulant Matrices

Fast Algorithms for Solving FLSR-Factor Block Circulant Linear Systems and Inverse Problem ofAX=b

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