Many complex problems rely on scientific and engineering computing for solutions. High-performance computing depends heavily on linear algebra for large scale data analysis, modeling and simulation, and other applied problems. Linear algebra provides the building blocks for a wide variety of scientific and engineering simulation codes. Sparse linear system solution often dominates the execution time of such applications, prompting the ongoing development of highly optimized iterative algorithms and high- performance parallel implementations. We are particularly interested in a scientific toolkit called Parallel Extensible Toolkit for Scientific Computation (PETSc) because of its efficiency, unique features and widespread popularity. In this report we present the algorithm classification results for the preconditioned iterative solvers in PETSc. In addition, we have created a comprehensive machine-learning-based workflow for the automated classification of iterative solvers, which can be generalized to other types of rapidly evolving numerical methods.