The Moore-Penrose Pseudoinverse of an Arbitrary, Square, k -circulant Matrix

Boman, Eugene

doi:10.1080/03081080290019559

Cited by 14 publications

(9 citation statements)

References 3 publications

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“…The k -permutation matrix P ^ can also be written as P ^ = cir c k [ 0 1 0 … 0 ] which signifies the fact that P ^ is a k-circulant matrix . We know from Boman (2002) that a k -circulant matrix can be diagonalized using Fourier matrix F and a diagonal matrix Ω …”

Section: Preliminaries Of K-circulant Matricesmentioning

confidence: 99%

A generalized hierarchical nearly cyclic pursuit for the leader-following consensus problem in multi-agent systems

Iqbal

Leth

Ngo

2017

Transactions of the Institute of Measurement and Control

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In this paper, we solve the leader-following consensus problem using a hierarchical nearly cyclic pursuit (HNCP) strategy for multi-agent systems. We extend the nearly cyclic pursuit strategy and the two-layer HNCP to the generalized L-layer HNCP that enables the agents to rendezvous at a point dictated by a beacon. We prove that the convergence rate of the generalized L-layer HNCP for the leader-following consensus problem is faster than that of the nearly cyclic pursuit. Simulation results demonstrate the effectiveness of the proposed method.

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Section: Preliminaries Of K-circulant Matricesmentioning

confidence: 99%

A generalized hierarchical nearly cyclic pursuit for the leader-following consensus problem in multi-agent systems

Iqbal

Leth

Ngo

2017

Transactions of the Institute of Measurement and Control

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“…Kou et al [2] discussed the ω-circulant preconditioners for solving the ill-conditioned block Toeplitz systems with tenser structure by using the preconditioned conjugate gradient (PCG) method. A simple derivation of the Moore-Penrose pseudoinverse of k-circulant matrix was given by Boman [3]. They provided a formula for the Moore-Penrose pseudoinverse of general n × n k-circulant matrix by displaying and exploiting the close relationship between the circulants and the k-circulants.…”

Section: Introductionmentioning

confidence: 99%

On computing of positive integer powers for r-circulant matrices

Jiang

Xin

Wang

2015

Applied Mathematics and Computation

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“…Namely, they proved the following theorem. They did not solve the problem of characterizing C † for an arbitrary k-circulant matrix C. That problem was solved by E. Boman in [3].…”

Section: Introductionmentioning

confidence: 99%

On k-circulant matrices with arithmetic sequence

Radičić

2017

Filomat

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Let k be a nonzero complex number. In this paper we consider k-circulant matrices with arithmetic sequence and investigate the eigenvalues, determinants and Euclidean norms of such matrices. Also, for k = 1, the inverses of such (invertible) matrices are obtained (in a way different from the way presented in [1]), and the Moore-Penrose inverses of such (singular) matrices are derived.2010 Mathematics Subject Classification. Primary 15B05; Secondary 11B25, 15A09, 15A15, 15A18, 15A60

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The Moore-Penrose Pseudoinverse of an Arbitrary, Square, k -circulant Matrix

Cited by 14 publications

References 3 publications

A generalized hierarchical nearly cyclic pursuit for the leader-following consensus problem in multi-agent systems

A generalized hierarchical nearly cyclic pursuit for the leader-following consensus problem in multi-agent systems

On computing of positive integer powers for r-circulant matrices

On k-circulant matrices with arithmetic sequence

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