Question

Variational method of accelerating linear iterations and its applications

Answer 1

An effective method for accelerating the convergence of iterative methods intended to solve ill-conditioned systems of algebraic equations is suggested. The method consists in error projection onto the space of residuals and is a generalized version of the method of steepest descent. Results of its application to the solution of systems of linear equations resulting from projection-grid approximations of stiff elliptical problems with small parameters at higher derivatives or significant singularities of domain geometry are presented and discussed. In addition, its application to some iterative finite-difference schemes for solution of two- and three-dimensional problems of aerodynamics is considered.