A study on quaternion blockquasi-tridiagonal systems

The objective of the present work is to study the solution of quaternion block quasi-tridiagonalsystems. Kershaw and Rózsa and Romani have proposed a method for calculating matrix inverses using second kind Chebyshev polynomials. This method has been generalized later to block tridiagonal matrices with quaternionic entries by Costa and Serôdio. In the present work, we make use of this method to solve block quasi-tridiagonal systems of the same kind. The computational effort to obtain the solution is evaluated, and future more efficient strategies are proposed.