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• Decomposing a Matrix into Circulant and Diagonal Factors.
• It is proven that if K does not equal F_3 or F_5 each square matrix with entries in K can be written as a product of circulant and diagonal matrices with entries in K. ...
• Keywords: Matrix factorization, diagonal and circulant matrices .

• Properties (nonexistence) of conference circulant matrices.
• A Hadamard matrix is called cyclic, iff it is written in standard form (first column and row contain only ones) and removing first row and column we obtain a circulant matrix. Is it possible to have Hadamard matrix which is circulant matrix? In this work we consider similar question, but concerning Conference matrices (it is the same as Hadamard, but the main diagonal is all zeroes). ... In 1 it is proved that Paley type Conference matrices are equivalent to circulant or negacirculant matrices. Therefore nonexistence of some Conference circulant matrices is essential. In this paper it is shown, that if Conference circulant matrix of order n exists, then the number n-1 is a square. ...

• The Digital Librarian's Digital Library searchDOCIS Documents in Computing and Information Science Home >> Journals and Conference Proceedings >> Information Processing Letters  Pancyclicity of recursive circulant graphs Toru Araki, Yukio Shibata  Journal Title: Information Processing Letters Date: 2002 Volume: 81 Issue: 4 p. ...

• Analytical Enumeration of Circulant Graphs with Prime-Squared Number of Vertices. ...
• A method for the analytical enumeration of circulant graphs with p2 vertices, p a prime, is proposed and described in detail. ... As a result, we get counting formulae and generating functions (by valency) for non-isomorphic p2-vertex directed and undirected circulant graphs as well as for some subclasses of them such as tournaments and self-complementary graphs. These are the first general enumerative results for circulant graphs for which the so-called ádám (single-multiplier) isomorphism condition does not hold. ...

• Circulant matrix.
• In linear algebra, a circulant matrix is a special kind of Toeplitz matrix where each row vector is shifted on element to the right relative to the preceding row vector. In other words a circulant matrix is an example of a Latin square. In numerical analysis circulant matrices are important because they can be quickly solved using the discrete fourier transform. ...
• 1 Definition 2 Properties 3 Solving circulant matrices 4 External link .
• is called a circulant matrix. ...
• Circulant matrices form an algebra, since for any two given circulant matrices A and B then the sum A+B is circulant, product AB is circulant, and AB = BA. ...
• The eigenvectors of a (square) circulant matrix of given size is fixed, that is, the eigenmatrix of a circulant matrix is the Fourier transform matrix of the same size. Consequently, the eigenvalues of a circulant matrix can be readily calculated by the Fast Fourier transform (FFT). ...
• If the FFT of the first row of a circulant matrix is performed then the determinant of the circulant matrix is the multiplication of the spectral values. ...
• C is an N by N circulant matrix .
• Solving circulant matrices.
• where C is a circulant square matrix of size n we can write the equation as the cyclic convolution .
• where c is the first row of the circulant matrix C and the vectors c, x and b are cyclically extended in each direction. ...
• Toeplitz and Circulant Matices: A Review, by R. ...

• Star Extremal Circulant Graphs.
• Star Extremal Circulant Graphs: SIAM Journal on Discrete Mathematics Vol. ... We prove that members of a certain family of circulant graphs are star extremal. ... We show relations between circulant graphs and distance graphs and discuss their star extremality. ... 330--339 on asymptotic independence ratios of circulant graphs. ...
• circular chromatic number, fractional chromatic number, circulant graph, distance graph, star extremal graph, independence ratio .

• 320 Distance-Hereditary Embeddings of Circulant Graphs .
• The members of this embedded set of rings are non-disjoint and preserve the minimal routing of the original circulant graph. Besides its practical consequences, our research allows the presentation of these optimal circulant graphs as a particular evolution of the traditional ring topology.   Index Terms- Circulant graphs, Chordal Rings, Cycles, Ádam’s Conjecture, Graph Embedding       .

• Circulant Matrix .
• Circulant matrices are examples of Latin Squares. ...
• See also Circulant Determinant .
• Circulant Matrices, 2nd ed. ...
• ``Brocard Points, Circulant Matrices, and Descartes' Folium. ...

• The Digital Librarian's Digital Library searchDOCIS Documents in Computing and Information Science Home >> Journals and Conference Proceedings >> Computing  Circulant Block-Factorization Preconditioning of Anisotropic Elliptic Problems Ivan Lirkov, Svetozar Margenov, L. ...

• Toeplitz and Circulant Matrices.
• Toeplitz and Circulant Matices: A Review, by R. ... ) but still occasionally useful tutorial on Toeplitz and circulant matrices. ...

• Chan, Circulant Preconditioners for Second Order Hyperbolic Equations, BIT 32, (1992) 650--664.
• Chan, Circulant Preconditioners for Second Order Hyperbolic Equations, BIT 32, (1992) 650--664. ...
• The convergence rate of the resulting preconditioned methods is also favorable and thoroughly analyzed in 101 Circulant preconditioners for second order hyperbolic equations have been considered by Jin and R. ... The coefficient matrix, obtained from an implicit time marching scheme, has condition number of O( 2 ) O(h Gamma2 ) With circulant type preconditioners, Jin and R. ...
• The convergence rate of the resulting preconditioned methods is also favorable and thoroughly analyzed in 101 Circulant preconditioners for second order hyperbolic equations have been considered by Jin and R. ... The coefficient matrix, obtained from an implicit time marching scheme, has condition number of O( 2 ) O(h Gamma2 ) With circulant type preconditioners, Jin and R. ...
• Chan, Circulant Preconditioners for Second Order Hyperbolic Equations, BIT, 32 (1992), pp. ...
• Circulant preconditioners for second order hyperbolic equations have been considered by Jin and R. ... The coefficient matrix, obtained from an implicit time marching scheme, has condition number of O( 2 ) O(h Gamma2 ) With circulant type preconditioners, Jin and R. ...
• Circulant preconditioners for second order hyperbolic equations have been considered by Jin and R. ... The coefficient matrix, obtained from an implicit time marching scheme, has condition number of O( 2 ) O(h Gamma2 ) With circulant type preconditioners, Jin and R. ...
• Chan, Circulant Preconditioners for Second Order Hyperbolic Equations, BIT, 32 (1992), pp. ...

• Discrete stochastic modelling of ATM-traffic with circulant transition matrices .
• Since the identification of a general MMPP is time consuming because of the large computational requirements, a circulant MMPP is used to reduce the computational cost. A circulant MMPP is an MMPP with a circulant transition matrix. ...
•   title={Discrete stochastic modelling of {ATM}-traffic with circulant transition matrices},.

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