marqLevAlg (version 1.1)

marqLevAlg-package: An algorithm for least-squares curve fitting.

Description

This algorithm provides a numerical solution to the problem of minimizing a function. This is more efficient than the Gauss-Newton-like algorithm when starting from points vey far from the final minimum. A new convergence test is implemented (RDM) in addition to the usual stopping criterion : stopping rule is when the gradients are small enough in the parameters metric (GH-1G).

Details

Package:	marqLevAlg
Type:	Package
Version:	1.1
Date:	2012-03-09
License:	GPL (>= 2.0)
LazyLoad:	yes

This algorithm provides a numerical solution to the problem of minimizing a function. This is more efficient than the Gauss-Newton-like algorithm when starting from points vey far from the final minimum. A new convergence test is implemented (RDM) in addition to the usual stopping criterion : stopping rule is when the gradients are small enough in the parameters metric (GH-1G).

References

marqLevAlg Algorithm

Donald W. marquardt An algorithm for Least-Squares Estimation of Nonlinear Parameters. Journal of the Society for Industrial and Applied Mathematics, Vol. 11, No. 2. (Jun, 1963), pp. 431-441.

Convergence criteria : Relative distance to Minimim

Commenges D. Jacqmin-Gadda H. Proust C. Guedj J. A Newton-like algorithm for likelihood maximization the robust-variance scoring algorithm arxiv:math/0610402v2 (2006)

Examples

# NOT RUN {
### 1
### initial values
b <- c(8,9)
### your function
f1 <- function(b){	
	return(4*(b[1]-5)^2+(b[2]-6)^2)	
}
## Call
test1 <- marqLevAlg(b=b,fn=f1)

### 2
### initial values
b <- c(3,-1,0,1)
### your function
f2 <- function(b){	
	return((b[1]+10*b[2])^2+5*(b[3]-b[4])^2+(b[2]-2*b[3])^4+10*(b[1]-b[4])^4)	
}

## Call
test2 <- marqLevAlg(b=b,fn=f2)
test2
# }