Parallel methods for finding stable approximate solutions to linear systems with perturbed right-hand sides

Some questions on the application of the theory of regularization of linear systems to applied problems of geophysics are considered. A number of ways for the reduction of original linear systems to systems in normal canonical form are proposed; as a result, new efficient iterative methods can be used. New orthogonal transformations for the construction of methods for finding stable approximate solutions are discussed. An analysis of the methods we proposed is given in the context of deep parallelization of computations and the efficient use of multiprocessor computing systems.