Efficient Iterative Solvers in the Least Squares Method
Paper i proceeding, 2020

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.

Convergence Acceleration of Richardson Iteration

Least Squares Estimation

High Order Newton-Schulz Algorithm

Simultaneous Calculations

Power Series Factorization Tool-Kit


Alexander Stotsky

Chalmers, Data- och informationsteknik, Software Engineering

IFAC Proceedings Volumes (IFAC-PapersOnline)

14746670 (ISSN)

Vol. 53 2 883-888

IFAC-V 2020
Berlin, Germany,


Annan data- och informationsvetenskap


Datavetenskap (datalogi)


Informations- och kommunikationsteknik



Beräkningsinfrastruktur för systembiologi

C3SE (Chalmers Centre for Computational Science and Engineering)


Grundläggande vetenskaper



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