IDR(s): A family of simple and fast algorithms for solving large nonsymmetric linear systems
Peter Sonneveld, Martin B. van Gijzen · Research Repository (Delft University of Technology) · 2007
We present IDR(s), a new family of efficient, short-recurrence methods for large nonsymmetric systems of linear equations.The new methods are based on the Induced Dimension Reduction (IDR) method proposed by Sonneveld in 1980.While state-ofthe-art methods such as Bi-CGSTAB require at most 2N matrix-vector products to compute an exact solution in exact arithmetic, IDR(s) requires at most N + N/s matrix-vector products, with N the problem size and s the dimension of a pre-chosen subspace.We describe the algorithm and the underlying theory and present numerical experiments to illustrate the theoretical properties of the method and its performance for systems arising from different applications.Our experiments show that IDR(s) is competitive with or superior to most Bi-CG-based methods, and outperforms Bi-CGSTAB when s > 1.