Error estimates on splitting systems of equations are mathematical tools used to quantify the accuracy and convergence properties of numerical methods for solving systems of equations. Splitting methods decompose a complex system into simpler subproblems, that can be solved iteratively. The error estimates provide insights into how the approximation differs from the exact solution and help assess the reliability of the numerical approach. When dealing with large and complex systems of equations, direct methods may be computationally expensive or impractical. Splitting methods offer an attractive alternative by breaking down the problem into smaller, more manageable parts. These methods include operator splitting, fractional-step methods, and iterative methods such as the alternating direction implicit (ADI) method. Error estimates on splitting systems of equations typically involve analyzing the convergence rate and the local and global errors of the numerical scheme. The convergence rate measures how quickly the numerical approximation approaches the true solution as the number of iterations increases.
