On the Adaptive Deterministic Multiple Row‐ and Column‐Action Methods

ABSTRACT

For solving the large‐scale linear system using iterative methods, we employ the Petrov‐Galerkin conditions and an adaptive heavy ball momentum technique, and introduce two deterministic multiple row‐ and column‐action methods. By exploiting a geometric property, we prove that the proposed methods achieve linear convergence rates, bounded by explicit expressions, and further obtain a yield tighter upper bounds on the convergence rate compared with non‐accelerated approaches. Numerical experiments and real‐world applications are provided to support the theoretical analysis and illustrate the practical effectiveness of the proposed methods.