Convergence Rate Improvement of Richardson and Newton-Schulz Iterations
Preprint, 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.

Tool-Kit for Matrix Power Series Factorization

Efficient Parallel Iterative Solvers

Computationally Efficient High Order Newton-Schulz and Richardson Algorithms

Convergence Acceleration of Richardson Iteration

Simultaneous Calculations

Least Squares

Författare

Alexander Stotsky

Chalmers, Data- och informationsteknik, Software Engineering

Styrkeområden

Energi

Fundament

Grundläggande vetenskaper

Ämneskategorier

Sannolikhetsteori och statistik

Reglerteknik

Signalbehandling

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2022-03-17