An elegant IDR(s) variant that efficiently exploits bi-orthogonality properties

The IDR(s) method that is proposed in [18] is a very efficient limited memory method for solving large nonsymmetric systems of linear equations. IDR(s) is based on the induced dimension reduction theorem, that provides a way to construct subsequent residuals that lie in a sequence of shrinking subspaces. The IDR(s) algorithm that is given in [18...

On the convergence behaviour of IDR(s)

An explanation is given of the convergence behaviour of the IDR(s) methods. The convergence of the IDR(s) algorithms has two components. The first consists of damping properties of certain factors in the residual polynomials, which becomes less important for large values of s. The second component depends on the behaviour of quasi-Lanczos...