A modification of the Dewilde–van der Veen method for inversion of finite structured matrices Original Research Article

We study a class of block structured matrices R={Rij}i,j=1N with a property that the solution of the corresponding system Rx=y of linear algebraic equations may be performed for O(N) arithmetic operations. In this paper for finite invertible matrices we analyze in detail factorization and inversion algorithms. These algorithms are related to those suggested by P.M. Dewilde and A.J. van der Veen (Time-varying Systems and Computations, Kluwer Academic Publishers, New York, 1998) for a class of finite and infinite matrices with a small Hankel rank. The algorithms presented here are more transparent and are a modification of the algorithms from the above reference. The approach and the proofs are essentially different from those in the above-mentioned reference. The paper contains also analysis of complexity and results of numerical experiments.