The inverses of some circulant matrices

A. Carmona, A.M. Encinas, S. Gago, M.J. Jiménez, M. Mitjana
2015 Applied Mathematics and Computation  
We present here necessary and sufficient conditions for the invertibility of circulant and symmetric matrices that depend on three parameters and moreover, we explicitly compute the inverse. The techniques we use are related with the solution of boundary value problems associated to second order linear difference equations. Consequently, we reduce the computational cost of the problem. In particular, we recover the inverses of some well known circulant matrices whose coefficients are arithmetic
more » ... or geometric sequences, Horadam numbers among others. We also characterize when a general symmetric circulant and tridiagonal matrix is invertible and in this case, we compute explicitly its inverse.
doi:10.1016/j.amc.2015.08.084 fatcat:4myiwkxznndmbfvnyfgh2ggvem