Nonlinear least-squares data fitting in Excel spreadsheets

The Mittag-Leffler relaxation function, [Formula: see text], with [Formula: see text], plays an important role in the fractional viscoelastic models. The Mittag-Leffler function is an infinite series whose analytic derivatives are unexplored, thus a direct search method based on Powell’s method is introduced to solve the minimization problem of nonlinear least-squares data fitting for Mittag-Leffler relaxation function in this paper. A simple and effective method is provided for the determination of the initial values and an acceleration strategy is proposed for this direct search method. Numerical results show this direct search method is efficient in the parameter estimation of the Mittag-Leffler relaxation function. Furthermore, the acceleration strategy proves to be conducive to improving the computational efficiency of this direct search method.

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A Recursive Bifurcation Model for Predicting the Peak of COVID-19 Virus Spread in United States and Germany

10.1101/2020.04.09.20059329 ◽

2020 ◽

Cited By ~ 3

Author(s):

Julia Shen

Keyword(s):

United States ◽

Decision Making ◽

South Korea ◽

Least Squares ◽

Nonlinear Least Squares ◽

Peak Time ◽

Virus Spread ◽

Linear Least Squares ◽

Least Squares Fitting ◽

Fitting In

AbstractPrediction on the peak time of COVID-19 virus spread is crucial to decision making on lockdown or closure of cities and states. In this paper we design a recursive bifurcation model for analyzing COVID-19 virus spread in different countries. The bifurcation facilitates a recursive processing of infected population through linear least-squares fitting. In addition, a nonlinear least-squares fitting is utilized to predict the future values of infected populations. Numerical results on the data from three countries (South Korea, United States and Germany) indicate the effectiveness of our approach.

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A recursive bifurcation model for early forecasting of COVID-19 virus spread in South Korea and Germany

Scientific Reports ◽

10.1038/s41598-020-77457-5 ◽

2020 ◽

Vol 10 (1) ◽

Author(s):

Julia Shen

Keyword(s):

South Korea ◽

Least Squares ◽

Nonlinear Least Squares ◽

Future Research ◽

Logistic Growth ◽

Virus Spread ◽

Least Squares Fitting ◽

Fitting Procedure ◽

Logistic Growth Model ◽

Fitting In

AbstractEarly forecasting of COVID-19 virus spread is crucial to decision making on lockdown or closure of cities, states or countries. In this paper we design a recursive bifurcation model for analyzing COVID-19 virus spread in different countries. The bifurcation facilitates recursive processing of infected population through linear least-squares fitting. In addition, a nonlinear least-squares fitting procedure is utilized to predict the future values of infected populations. Numerical results on the data from two countries (South Korea and Germany) indicate the effectiveness of our approach, compared to a logistic growth model and a Richards model in the context of early forecast. The limitation of our approach and future research are also mentioned at the end of this paper.

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