A note on the O(n)-storage implementation of the GKO algorithm
It offers an incremental improvement in memory efficiency for solving Cauchy-like linear systems, which is relevant for numerical linear algebra practitioners.
The paper proposes an O(n)-space implementation of the GKO-Cauchy algorithm for solving linear systems with Cauchy-like matrices, which outperforms existing algorithms for matrices larger than about 500-1000 due to better cache memory usage.
We propose a new O(n)-space implementation of the GKO-Cauchy algorithm for the solution of linear systems with Cauchy-like matrix. Despite its slightly higher computational cost, this new algorithm makes a more efficient use of the processor cache memory. Thus, for matrices of size larger than about 500-1000, it outperforms the existing algorithms. We present an applicative case of Cauchy-like matrices with non-reconstructible main diagonal. In this special instance, the O(n) space algorithms can be adapted nicely to provide an efficient implementation of basic linear algebra operations in terms of the low displacement-rank generators.