Convergence Rate Improvement of Richardson and Newton-Schulz Iterations
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
Computationally Efficient High Order Newton-Schulz and Richardson Algorithms
Chalmers, Computer Science and Engineering (Chalmers), Software Engineering (Chalmers)
Areas of Advance
Probability Theory and Statistics