On the minimal residual methods for solving diffusion-convection SLAEs

Abstract The objective of this research is to develop and study iterative methods in the Krylov subspaces for solving systems linear algebraic equations (SLAEs) with non-symmetric sparse matrices high orders arising approximation multi-dimensional boundary value problems on unstructured grids. These are also relevant many applications, including diffusion-convection equations. considered algorithms based constructing A T — orthogonal direction vectors calculated using short recursions providing global minimization a residual at each iteration. Methods Lanczos orthogonalization, preconditioned conjugate residuals algorithm, as well left Gauss transform original SLAEs implemented. In addition, efficiency these processes investigated when an approximate factorization matrix Eisenstat modification. results set computational experiments various grids values convective coefficients presented, which demonstrate sufficiently approaches under consideration.