Induced Dimension Reduction algorithms for solving non-symmetric sparse matrix problems

In several applications in science and engineering, different types of matrix problems emerge from the discretization of partial differential equations.<br/>This thesis is devoted to the development of new algorithms to solve this<br/>kind of problems. In particular, when the matrices involved are sparse and<br/>non-symmetric. The new algorithms...

Induced Dimension Reduction method for solving linear matrix equations

This paper discusses the solution of large-scale linear matrix equations using the Induced Dimension reduction method (IDR(s)). IDR(s) was originally presented to solve system of linear equations, and is based on the IDR(s) theorem. We generalize the IDR(s) theorem to solve linear problems in any finite-dimensional space. This generalization...

Exploiting BiCGstab(?) strategies to induce dimension reduction

IDR(s) [P. Sonneveld and M. B. van Gijzen, SIAM J. Sci. Comput., 31 (2008), pp. 1035–1062] and BiCGstab(?) [G. L. G. Sleijpen and D. R. Fokkema, Electron. Trans. Numer. Anal., 1 (1993), pp. 11–32] are two of the most efficient short-recurrence iterative methods for solving large nonsymmetric linear systems of equations. Which of the two is best...