Abstract: The nonlinear least squares problem has the general formmin{r(x):x∈ℝn},where r is the function defined byr(x)=12‖ƒ(x)‖22for some vector-valued function ƒ that maps ℝn to ℝm .Least squares problems often arise in data-fitting applications. Suppose that some physical or economic process is modeled by a nonlinear function ϕ that depends on a parameter vector x and time t. If bi is the actual output of the system at time ti , then the residualϕ(x,ti)−bimeasures the discrepancy between the predicted and observed outputs of the system at time ti . A reasonable estimate for the parameter x may be obtained by defining the ith component of ƒ by ƒi(x)=ϕ(x,ti)−bi , and solving the least squares problem with this definition of ƒ.
Publication Year: 1993
Publication Date: 1993-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 1
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