Unified frameworks for high order Newton-Schulz and Richardson iterations: a computationally efficient toolkit for convergence rate improvement
Journal article, 2019
Convergence rate and robustness improvement
together with reduction of computational
complexity are required for solving the system
of linear equations in many applications such as
system identification, signal and image processing, network
analysis, machine learning and many others.
Two unified frameworks (1) for convergence
rate improvement of high order Newton-Schulz
matrix inversion algorithms and (2) for combination of
Richardson and iterative matrix inversion algorithms with
improved convergence rate for estimation of the parameter vector are proposed.
Recursive and computationally efficient version of new algorithms
is developed for implementation on parallel computational units.
In addition to unified description of the algorithms the
frameworks include explicit transient models of estimation errors
and convergence analysis.
Simulation results confirm significant performance improvement of proposed
algorithms in comparison with existing methods.
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