Generalised matrix inversion and rank computation by successive matrix powering

Learning Representation and Control in Markov Decision Processes: New Frontiers

“…To compute the Drazin bases using the Schultz expansion, we will use an iterative method called Successive Matrix Squaring (SMS) that was developed for efficient parallel implementation of general inverses of matrices [141,25]. Note that from the definition of Drazin inverse in Section 3.3.3, we note that if X is a Drazin inverse of A, then it must satisfy the following properties:…”

“…Parallel implementations for computing pseudo-inverses in general, and the Drazin inverse in particular, have been developed. These methods enabled generalized inverses can be computed in O(log 2 n), assuming there are sufficient processors to compute matrix multiplication in O(log n) [25,141]. This parallel algorithm uses an iterative method to compute the Drazin inverse.…”

Convergence of Rump’s method for computing the Moore-Penrose inverse

“…A number of numerical and symbolic algorithms, see [5], [6], [19], [20], [36] for computing the Moore-Penrose inverse of the structured and block matrices have been presented. Rump et al develop the numerically verified methods for the matrix inversion, see [24], [26], [29], [33], the matrix equations in [25], the linear least squares problem and the under-determined linear system in [28].…”

Effective algorithms of the Moore-Penrose inverse matrices for extreme learning machine

“…There are several methods for computing the Moore-Penrose inverse matrices [20]. These may include orthogonal projection, orthogonalization method, iterative method, and singular value decomposition (SVD) [21][22][23][24][25][26][27][28]. The orthogonalization method and iterative method have their limitations since searching and iteration are used.…”