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# NonLinearLeastSquare

## NAME

NonLinearLeastSquare â

Non-linear least-square method.

## SYNOPSIS

#include <ql/math/optimization/leastsquare.hpp>

Public Member Functions

NonLinearLeastSquare (Constraint &c, Real accuracy=1e-4, Size maxiter=100)
Default constructor.

NonLinearLeastSquare
(Constraint &c, Real accuracy, Size maxiter, boost::shared_ptr< OptimizationMethod > om)
Default constructor.

~NonLinearLeastSquare
()
Destructor.

Array
& perform (LeastSquareProblem &lsProblem)
Solve least square problem using numerix solver.

void setInitialValue (const Array &initialValue)
Array
& results ()
return the results

Real residualNorm
()
return the least square residual norm

Real lastValue
()
return last function value

Integer exitFlag
()
return exit flag

Integer iterationsNumber
()
return the performed number of iterations

## Detailed Description

Non-linear least-square method.

Using a given optimization algorithm (default is conjugate gradient),

min r(x) : x in R^n ]

where rm#229 is the Euclidean norm of rm#230@_fakenl for some vector-valued function rm#37 from

\$ R^n \$ to \$ R^m \$, f = (f_1, ..., f_m) ] with \$ f_i(x) = b_i - hi(x,t_i) \$ where \$ b \$ is the vector of target data and \$ phi \$ is a scalar function.

Assuming the differentiability of \$ f \$, the gradient of \$ r \$ is defined by grad r(x) = fâ(x)^t.f(x) ]

## Author

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