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Preconditioning of conjugate gradients by multigrid solver

Jitka Křížková, Petr Vaněk (1994)

Applications of Mathematics

Solving a system of linear algebraic equations by the preconditioned conjugate gradient method requires to solve an auxiliary system of linear algebraic equations in each step. In this paper instead of solving the auxiliary system one iteration of the two level method for the original system is done.

Preconditioning of two-by-two block matrix systems with square matrix blocks, with applications

Owe Axelsson (2017)

Applications of Mathematics

Two-by-two block matrices of special form with square matrix blocks arise in important applications, such as in optimal control of partial differential equations and in high order time integration methods. Two solution methods involving very efficient preconditioned matrices, one based on a Schur complement reduction of the given system and one based on a transformation matrix with a perturbation of one of the given matrix blocks are presented. The first method involves an additional inner solution...

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