Advanced Equation System Solver: Handling Overdetermined and Ill-Conditioned Equations

During my project development, I encountered challenging numerical problems including overdetermined equations and ill-conditioned systems. To address these issues, I developed an advanced equation system solver that efficiently handles various matrix scenarios. The implementation features robust algorithms for computing least-squares solutions using methods like QR decomposition or singular value decomposition (SVD) for enhanced numerical stability. Key functions include matrix rank detection, condition number calculation, and automated regularization techniques for ill-conditioned systems. The program offers multiple matrix factorization options and includes comprehensive error handling. With an intuitive user interface and detailed documentation, the solver provides both command-line and API access for seamless integration. I welcome feedback and suggestions to further enhance its capabilities and performance for the computational mathematics community.