The residual cutting (RC) method has been proposed as an outer–inner loop iteration for
efficiently solving large and sparse linear systems of equations arising from the numerical solution of
elliptic partial differential equations. Based on RC, the generalized residual cutting (GRC) method
has been introduced, which can be applied to more general sparse linear system problems. In this
paper, we show that GRC can stabilize BiCGSTAB, which is an iterative algorithm for solving large,
sparse, and nonsymmetric linear systems and is widely used in scientific computing and engineering
simulations due to its robustness. BiCGSTAB converges faster and more smoothly than the original
BiCG method by reducing irregular convergence behavior through residual stabilization. However,
it sometimes fails to converge due to stagnation or breakdown. In this work, we attempt to enhance
its robustness by further stabilizing it using GRC, thereby avoiding such failures.
