3 research outputs found
Flexible Enlarged Conjugate Gradient Methods
Enlarged Krylov subspace methods and their s-step versions were introduced
[7] in the aim of reducing communication when solving systems of linear
equations Ax = b. These enlarged CG methods consist of enlarging the Krylov
subspace by a maximum of t vectors per iteration based on the domain
decomposition of the graph of A. As for the s-step versions, s iterations of
the enlarged Conjugate Gradient methods are merged in one iteration. The
Enlarged CG methods and their s-step versions converge in less iterations than
the classical CG, but at the expense of requiring more memory storage than CG.
Thus in this paper we explore different options for reducing the memory
requirements of these enlarged CG methods without affecting much their
convergence.Comment: 28 pages, 14 figure
Data-Driven Models for studying the Dynamics of the COVID-19 Pandemics
This paper seeks to study the evolution of the COVID-19 pandemic based on
daily published data from Worldometer website, using a time-dependent SIR
model. Our findings indicate that this model fits well such data, for different
chosen periods and different regions. This well-known model, consisting of
three disjoint compartments, susceptible , infected , and removed , depends in
our case on two time dependent parameters, the infection rate and
the removal rate . After deriving the model, we prove the local
exponential behavior of the number of infected people, be it growth or decay.
Furthermore, we extract a time dependent replacement factor , where is the ratio of susceptible people at
time . In addition, and are respectively the ratios of
infected and removed people, based on a population of size , usually assumed
to be constant. Besides these theoretical results, the report provides
simulations on the daily data obtained for Germany, Italy, and the entire
World, as collected from Worldometer over the period stretching from April 2020
to June 2022. The computational model consists of the estimation of ,
and based on the time-dependent SIR model. The validation of
our approach is demonstrated by comparing the profiles of the collected data and those obtained from the SIR model with the approximated
parameters. We also consider matching the data with a constant-coefficient SIR
model, which seems to be working only for short periods. Thus, such model helps
understanding and predicting the evolution of the pandemics for short periods
of time where no radical change occurs.Comment: 59 page