An Efficient and Generic Algorithm for Matrix Inversion

This work presents an improvement on the simple algorithms of matrix inversion (Farooq & Hamid, 2010). This generalized algorithm supports selection of pivot randomly in the matrix thus supporting partial and full pivoting. The freedom in pivot selection can be used in minimizing the numerical error and prioritizing the variable to find the solution first. The algorithm is more suitable for finding inverse and determinant of dense matrices. The algorithm requires a mechanism for selection of pivot (e.g., selection of absolute maximum value) in the available sub-matrix and the mechanism to get the inverse from the final resultant matrix by rearranging the rows and columns. A method for assigning the sign of the determinant is also given. The algorithm is explained through solved examples. The number of arithmetic calculations performed by the algorithm is of O (n ) however. The efficiency and simplicity of coding remains the same as of the original algorithm. DOI: 10.4018/978-1-4666-1752-0.ch008