Multiple solution of systems of linear algebraic equations by an iterative method with the adaptive recalculation of the preconditioner

The mean time needed to solve a series of systems of linear algebraic equations (SLAEs) as a function of the number of SLAEs is investigated. It is proved that this function has an extremum point. An algorithm for adaptively determining the time when the preconditioner matrix should be recalculated when a series of SLAEs is solved is developed. A numerical experiment with multiply solving a series of SLAEs using the proposed algorithm for computing 100 capacitance matrices with two different structures — microstrip when its thickness varies and a modal filter as the gap between the conductors varies — is carried out. The speedups turned out to be close to the optimal ones.