Efficient stand-alone generalized inverse algorithms and software for engineering/sciences applications: Research and education

Efficient numerical procedures for finding the generalized (or pseudo) inverse of a general (square/rectangle, symmetrical/unsymmetrical, non-singular/singular, real/complex numbers) matrix and solving systems of Simultaneous Linear Equations (SLE) are formulated and explained. The developed procedures and its associated computer software (under MATLAB computer environment) have been based on "special Cholesky factorization schemes" (for a singular matrix), the generalized inverse of the matrix product, and were further enhanced by the Domain Decomposition (DD) formulation.;Test matrices from different fields of applications have been chosen, tested and compared with other existing algorithms. The results of the numerical tests have indicated that the developed procedures are far more efficient than existing algorithms. Furthermore, an educational version of the generalized inverse algorithms and software for solving SLE has also been developed to run any FORTRAN and/or 'C' programs over the web. This developed technology and software is freely available and can run on any device with interne connectivity and browser capability.