An Improved Computationally Efficient Method for Finding the Drazin Inverse

Jebreen, Haifa Bin; Chalco-Cano, Y.

doi:10.1155/2018/6758302

Cited by 3 publications

(1 citation statement)

References 24 publications

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“…Fast and computationally efficient algorithms can be designed in this case. Consider algorithm (26) with T 1 = T 2 = ... = T k , where T k and Γ k are defined in (32), (33) with w = n and x i = hn k , h, n = 1, 2, ... :…”

Section: Double Newton-schulz Algorithm With High Order Residual As C...mentioning

confidence: 99%

Convergence Rate Improvement of Richardson and Newton-Schulz Iterations

Stotsky

2020

Preprint

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Fast convergent, accurate, computationally efficient, parallelizable, and robust matrix inversion and parameter estimation algorithms are required in many time-critical and accuracy-critical applications such as system identification, signal and image processing, network and big data analysis, machine learning and in many others. This paper introduces new composite power series expansion with optionally chosen rates (which can be calculated simultaneously on parallel units with different computational capacities) for further convergence rate improvement of high order Newton-Schulz iteration. New expansion was integrated into the Richardson iteration and resulted in significant convergence rate improvement. The improvement is quantified via explicit transient models for estimation errors and by simulations. In addition, the recursive and computationally efficient version of the combination of Richardson iteration and Newton-Schulz iteration with composite expansion is developed for simultaneous calculations. Moreover, unified factorization is developed in this paper in the form of tool-kit for power series expansion, which results in a new family of computationally efficient Newton-Schulz algorithms.

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Section: Double Newton-schulz Algorithm With High Order Residual As C...mentioning

confidence: 99%

Convergence Rate Improvement of Richardson and Newton-Schulz Iterations

Stotsky

2020

Preprint

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A Seventh-Order Scheme for Computing the Generalized Drazin Inverse

et al. 2019

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One of the most important generalized inverses is the Drazin inverse, which is defined for square matrices having an index. The objective of this work is to investigate and present a computational tool in the form of an iterative method for computing this task. This scheme reaches the seventh rate of convergence as long as a suitable initial matrix is chosen and by employing only five matrix products per cycle. After some analytical discussions, several tests are provided to show the efficiency of the presented formulation.

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Calculating the Weighted Moore–Penrose Inverse by a High Order Iteration Scheme

Jebreen

2019

Mathematics

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The goal of this research is to extend and investigate an improved approach for calculating the weighted Moore-Penrose (WMP) inverses of singular or rectangular matrices. The scheme is constructed based on a hyperpower method of order ten. It is shown that the improved scheme converges with this rate using only six matrix products per cycle. Several tests are conducted to reveal the applicability and efficiency of the discussed method, in contrast with its well-known competitors.

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An Improved Computationally Efficient Method for Finding the Drazin Inverse

Cited by 3 publications

References 24 publications

Convergence Rate Improvement of Richardson and Newton-Schulz Iterations

Convergence Rate Improvement of Richardson and Newton-Schulz Iterations

A Seventh-Order Scheme for Computing the Generalized Drazin Inverse

Calculating the Weighted Moore–Penrose Inverse by a High Order Iteration Scheme

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