Project Euclid

References

• A. C. Wilde, “Differential equations involving circulant matrices,” The Rocky Mountain Journal of Mathematics, vol. 13, no. 1, pp. 1–13, 1983.
  Mathematical Reviews (MathSciNet): MR692571
  Zentralblatt MATH: 0516.34016
  Digital Object Identifier: doi:10.1216/RMJ-1983-13-1-1
  Project Euclid: euclid.rmjm/1250128024
  
• B. Voorhees and A. Nip, “Ordinary differential equations with star structure,” Journal of Dynamical Systems and Geometric Theories, vol. 3, no. 2, pp. 121–152, 2005.
  Mathematical Reviews (MathSciNet): MR2180759
  Zentralblatt MATH: 1096.34005
  Digital Object Identifier: doi:10.1080/1726037X.2005.10698495
  
• C. Zhang, H. Chen, and L. Wang, “Strang-type preconditioners applied to ordinary and neutral differential-algebraic equations,” Numerical Linear Algebra with Applications, vol. 18, no. 5, pp. 843–855, 2011.
  Mathematical Reviews (MathSciNet): MR2833818
  Zentralblatt MATH: 1249.65165
  Digital Object Identifier: doi:10.1002/nla.770
  
• M. P. Joy and V. Tavsanoglu, “Circulant matrices and the stability of a class of CNNs,” International Journal of Circuit Theory and Applications, vol. 24, no. 1, pp. 7–13, 1996.
• J. Delgado, N. Romero, A. Rovella, and F. Vilamajó, “Bounded solutions of quadratic circulant difference equations,” Journal of Difference Equations and Applications, vol. 11, no. 10, pp. 897–907, 2005.
  Mathematical Reviews (MathSciNet): MR2173720
  Zentralblatt MATH: 1097.37011
  Digital Object Identifier: doi:10.1080/10236190500138312
  
• X.-Q. Jin, V.-K. Sin, and L.-l. Song, “Circulant-block preconditioners for solving ordinary differential equations,” Applied Mathematics and Computation, vol. 140, no. 2-3, pp. 409–418, 2003.
  Mathematical Reviews (MathSciNet): MR1953912
  Zentralblatt MATH: 1044.65062
  Digital Object Identifier: doi:10.1016/S0096-3003(02)00237-0
  
• P. J. Davis, Circulant Matrices, Pure and Applied Mathematics, John Wiley & Sons, New York, NY, USA, 1979.
  Mathematical Reviews (MathSciNet): MR543191
  
• R. M. Gray, “Toeplitz and circulant matrices: A review,” Foundations and Trends in Communications and Information Theory, vol. 2, no. 3, pp. 155–239, 2006.
• Z. L. Jiang and Z. X. Zhou, Circulant Matrices, Chengdu Technology University, Chengdu, China, 1999.
• A. Bose, R. S. Hazra, and K. Saha, “Poisson convergence of eigenvalues of circulant type matrices,” Extremes, vol. 14, no. 4, pp. 365–392, 2011.
  Mathematical Reviews (MathSciNet): MR2853107
  Digital Object Identifier: doi:10.1007/s10687-010-0115-5
  
• A. Bose, R. S. Hazra, and K. Saha, “Spectral norm of circulant-type matrices,” Journal of Theoretical Probability, vol. 24, no. 2, pp. 479–516, 2011.
  Mathematical Reviews (MathSciNet): MR2795050
  Zentralblatt MATH: 1241.60006
  Digital Object Identifier: doi:10.1007/s10959-009-0257-z
  
• C. Erbas and M. M. Tanik, “Generating solutions to the $N$-queens problem using $g$-circulants,” Mathematics Magazine, vol. 68, no. 5, pp. 343–356, 1995.
  Mathematical Reviews (MathSciNet): MR1365646
  Digital Object Identifier: doi:10.2307/2690923
  
• Y.-K. Wu, R.-Z. Jia, and Q. Li, “$g$-circulant solutions to the $(0,1)$ matrix equation ${A}^{m}={J}_{n}$,” Linear Algebra and Its Applications, vol. 345, pp. 195–224, 2002.
  Mathematical Reviews (MathSciNet): MR1883273
  Zentralblatt MATH: 0998.15015
  Digital Object Identifier: doi:10.1016/S0024-3795(01)00491-8
  
• E. Ngondiep, S. Serra-Capizzano, and D. Sesana, “Spectral features and asymptotic properties for $g$-circulants and $g$-Toeplitz sequences,” SIAM Journal on Matrix Analysis and Applications, vol. 31, no. 4, pp. 1663–1687, 2009/10.
  Mathematical Reviews (MathSciNet): MR2644732
  Digital Object Identifier: doi:10.1137/090760209
  
• S. Falcon and A. Plaza, “On $k$-Fibonacci numbers of arithmetic indexes,” Applied Mathematics and Computation, vol. 208, no. 1, pp. 180–185, 2009.
  Mathematical Reviews (MathSciNet): MR2490783
  Digital Object Identifier: doi:10.1016/j.amc.2008.11.031
  
• Y. Yazlik and N. Taskara, “A note on generalized $k$-Horadam sequence,” Computers & Mathematics with Applications, vol. 63, no. 1, pp. 36–41, 2012.
  Mathematical Reviews (MathSciNet): MR2863474
  
• S.-Q. Shen, J.-M. Cen, and Y. Hao, “On the determinants and inverses of circulant matrices with Fibonacci and Lucas numbers,” Applied Mathematics and Computation, vol. 217, no. 23, pp. 9790–9797, 2011.
  Mathematical Reviews (MathSciNet): MR2811251
  Zentralblatt MATH: 1222.15010
  Digital Object Identifier: doi:10.1016/j.amc.2011.04.072
  
• A. Cambini, “An explicit form of the inverse of a particular circulant matrix,” Discrete Mathematics, vol. 48, no. 2-3, pp. 323–325, 1984.
  Mathematical Reviews (MathSciNet): MR737275
  Zentralblatt MATH: 0531.15001
  Digital Object Identifier: doi:10.1016/0012-365X(84)90192-4
  
• D. Bozkurt and T.-Y. Tam, “Determinants and inverses of circulant matrices with Jacobsthal and Jacobsthal-Lucas Numbers,” Applied Mathematics and Computation, vol. 219, no. 2, pp. 544–551, 2012.
  Mathematical Reviews (MathSciNet): MR2956985
  Zentralblatt MATH: 06284149
  Digital Object Identifier: doi:10.1016/j.amc.2012.06.039
  
• W. T. Stallings and T. L. Boullion, “The pseudoinverse of an $r$-circulant matrix,” Proceedings of the American Mathematical Society, vol. 34, pp. 385–388, 1972. \endinput
  Mathematical Reviews (MathSciNet): MR0296082