%0 Journal Article %1 carmona15 %A Carmona, A. %A Encinas, A.M. %A Gago, S. %A Jiménez, M.J. %A Mitjana, M. %C New York, NY, USA %D 2015 %I Elsevier Science Inc. %J Appl. Math. Comput. %K circulant matrix no.pdf %N C %P 785--793 %R 10.1016/j.amc.2015.08.084 %T The Inverses of Some Circulant Matrices %V 270 %X We present here necessary and sufficient conditions for the invertibility of some circulant matrices that depend on three parameters and moreover, we explicitly compute the inverse. Our study also encompasses a wide class of circulant symmetric matrices. 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 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.

@article{carmona15, abstract = {We present here necessary and sufficient conditions for the invertibility of some circulant matrices that depend on three parameters and moreover, we explicitly compute the inverse. Our study also encompasses a wide class of circulant symmetric matrices. 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 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.}, acmid = {2839734}, added-at = {2017-06-07T09:27:20.000+0200}, address = {New York, NY, USA}, author = {Carmona, A. and Encinas, A.M. and Gago, S. and Jim{\'e}nez, M.J. and Mitjana, M.}, biburl = {https://www.bibsonomy.org/bibtex/2bbb0178a91929e15c4c03a10cf55a14c/ytyoun}, description = {The inverses of some circulant matrices}, doi = {10.1016/j.amc.2015.08.084}, interhash = {bb5e8a77cc13150a34b59a98e516e35b}, intrahash = {bbb0178a91929e15c4c03a10cf55a14c}, issn = {0096-3003}, issue_date = {November 2015}, journal = {Appl. Math. Comput.}, keywords = {circulant matrix no.pdf}, month = nov, number = {C}, numpages = {9}, pages = {785--793}, publisher = {Elsevier Science Inc.}, timestamp = {2017-06-07T09:27:20.000+0200}, title = {The Inverses of Some Circulant Matrices}, volume = 270, year = 2015 }