Unified frameworks for high order Newton-Schulz and Richardson iterations: a computationally efficient toolkit for convergence rate improvement

Convergence rate and robustness improvement together with reduction of computational complexity are required for solving the system of linear equations A θ ∗ = b in many applications such as system identification, signal and image processing, network analysis, machine learning and many others. Two u...

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Bibliographic Details
Published in:	Journal of applied mathematics & computing Vol. 60; no. 1-2; pp. 605 - 623
Main Author:	Stotsky, Alexander
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2019 Springer Nature B.V
Subjects:	Algorithms Applied mathematics Brief Reports Computational efficiency Computational Mathematics and Numerical Analysis Computer simulation Convergence Image processing Iterative methods Linear equations Machine learning Markov analysis Mathematical and Computational Engineering Mathematics Mathematics and Statistics Mathematics of Computing Network analysis Richardson iteration · Neumann series · High order Newton-Schulz algorithm · Least squares estimation · Harmonic regressor · Strictly Diagonally Dominant Matrix · Symmetric positive definite matrix · Ill-conditioned matrix · Polynomial preconditioning · Matrix power series factorization · Computationally efficient matrix inversion algorithm · Simultaneous calculations Robustness (mathematics) Signal processing System identification Theory of Computation Computationally efficient matrix inversion algorithm Richardson iteration Strictly Diagonally Dominant Matrix Ill-conditioned matrix Polynomial preconditioning Symmetric positive definite matrix Simultaneous calculations Least squares estimation Neumann series High order Newton-Schulz algorithm Matrix power series factorization Harmonic regressor
ISSN:	1598-5865, 1865-2085
Online Access:	Get full text
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