Conjugate direction methods for multiple solution of SLAEs

Conjugate gradient and conjugate residual methods for multiple solution of systems of linear algebraic equations (SLAE) with the same matrices but with different successively determined right-hand sides are considered. In order to speed up the iterative processes when solving the second and subsequent SLAEs, deflation algorithms are applied. These algorithms use the direction vectors obtained in the course of solving the first system as the basis vectors. Results of numerical experiments for model examples, illustrating the efficiency of the approaches under consideration, are provided.