Randomized vector iterative linear solvers of high precision for large dense system
-
Karl K. Sabelfeld
and
Anastasiya Kireeva
Abstract
In this paper we suggest randomized linear solvers with a focus on refinement issue to achieve a high precision while maintaining all the advantages of the Monte Carlo method for solving systems of large dimension with dense matrices. It is shown that each iterative refinement step reduces the error by one order of magnitude. The crucial point of the suggested method is, in contrast to the standard Monte Carlo method, that the randomized vector algorithm computes the entire solution column at once, rather than a single component. This makes it possible to efficiently construct the iterative refinement method. We apply the developed method for solving a system of elasticity equations.
Funding source: Russian Science Foundation
Award Identifier / Grant number: 19-11-00019
Funding statement: Support by the Russian Science Foundation under Grant 19-11-00019 is greatly acknowledged.
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Articles in the same Issue
- Frontmatter
- Analysis of wall-modelled particle/mesh PDF methods for turbulent parietal flows
- Stochastic simulation of electron transport in a strong electrical field in low-dimensional heterostructures
- Randomized vector iterative linear solvers of high precision for large dense system
- On the stationarity and existence of moments of the periodic EGARCH process
- Statistical analysis of the estimates of some stationary performances of the unreliable M/M/1/N queue with Bernoulli feedback
Articles in the same Issue
- Frontmatter
- Analysis of wall-modelled particle/mesh PDF methods for turbulent parietal flows
- Stochastic simulation of electron transport in a strong electrical field in low-dimensional heterostructures
- Randomized vector iterative linear solvers of high precision for large dense system
- On the stationarity and existence of moments of the periodic EGARCH process
- Statistical analysis of the estimates of some stationary performances of the unreliable M/M/1/N queue with Bernoulli feedback
