The efficient solution of large, sparse linear systems is a central problem in many fields of engineering and scientific computing. While direct methods such as Gaussian elimination or LU factorization are robust, they quickly become prohibitively expensive in terms of memory and computational cost for the increasing number of larger-scale problems. Iterative Krylov subspace methods have therefore become the de facto standard in such settings. However, due to the diversity of the different Krylov methods, choosing an appropriate one is highly dependent on the specific problem and available computational resources. In this thesis, we focus on the Induced imensionReductionmethodIDR(s), introduced by Sonneveld and van Gijzen (2008), which generalizes the original IDR method developed in 1980 by Wesseling and Sonneveld, and promises improved convergence behavior by constructing residuals within nested subspaces of decreasing dimension. Weimplemented IDR(s) as a new Krylov solver in the PETSc library, with careful attention to integration into its Krylov Subspace Solver (KSP)framework. This mainly consisted in writing the method according to the KSP interface, thus creating a new solver type that we called idrs. Our implementation was then benchmarked against widely used methods such as Conjugate Gradient Squared (CGS), GMRES, and BiCGStab, using a collection of real-world matrices from the SuiteSparse Matrix Collection. The experiments investigate both general robustness and performance as well as the influence of the shadow space dimensions and the choice of the shadow-space matrix P. The results show that IDR(s) is competitive with state-of-the-art Krylov solvers, even surpassing them in pure convergence rate over a set of general matrices. In many cases, moderate values of s (e.g., s = 4 or s = 8) provide a favorable trade-off between convergence speed and robustness. Furthermore, our experiments confirm several of the claims made in the original literature, such as the theoretical bound on convergence steps and the sensitivity to the conditioning of the small s × s systems. These findings support IDR(s) as a practical addition to PETSc for solving large, sparse linear systems in a black-box environment