Parallel changing triangular iterative methods in Krylov subspaces

The paper considers parallel preconditioned iterative methods in Krylov subspaces for solving large systems of linear algebraic equations with sparse symmetric positive-definite matrices arising in grid approximations of multidimensional problems. For preconditioning, generalized block algorithms of symmetric successive overrelaxation or incomplete factorization with matching row sums are used. Preconditioners are based on changing triangular matrix factors with multiple changes in the triangulation structure. In three-dimensional grid algebraic systems, methods are based on nested factorizations, as well as on two-level iterative processes. Successive approximations in Krylov subspaces are computed by applying a family of conjugate direction algorithms with various orthogonal and variational properties, including preconditioned conjugate gradient methods, conjugate residuals, and minimal errors.