Convergence Rate Improvement of Richardson and Newton-Schulz Iterations
Report, 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

Convergence Acceleration of Richardson Iteration

Efficient Parallel Iterative Solvers

Simultaneous Calculations

Computationally Efficient High Order Newton-Schulz and Richardson Algorithms

Least Squares


Alexander Stotsky

Chalmers, Computer Science and Engineering (Chalmers), Software Engineering (Chalmers)

Areas of Advance



Basic sciences

Subject Categories

Probability Theory and Statistics

Control Engineering

Signal Processing

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