Neurocomputing-Based Matrix Inversion: A Critical Review of the Related State of the Art

Solving matrix inversion is very useful in many areas of science (e.g., in physics and engineering, such as chemical processes, robotics, electronic circuits, engineered materials, and other natural sciences). Various methods exist to solve matrix inversion problems. Most of them are very good algorithms, which, however, have the drawback of being efficient only when implemented on single-processor systems. Therefore, those algorithms are very inefficient when implemented on multiprocessor platforms; thus, they lack sufficient parallelizability. The main root of the problem lies in the nature of the algorithms, since they were originally designed for implementations on single-processor systems. Some novel concepts involving neurocomputing, however, have the potential for more efficiency in multicore environments. This chapter provides a comprehensive overview of both traditional and neurocomputing-based methods for solving the matrix inversion problem (i.e., analytical, heuristics, dynamical-system-based methods, etc.). These methods are compared based on some important criteria including convergence, parallelizability/scalability, accuracy, and applicability to time-varying matrices. Finally, we propose a new concept based on neurocomputing for solving the matrix inversion problem. The main advantage of this concept is the possibility of efficiently satisfying all the important criteria.