Full Newton and constraint methods for semilinear signal modeling

The authors derive an expression for the Hessian matrix of the variable projection functional (VPF) and implement the Hessian using QR factorization. This is incorporated into a full Newton variable projection (FNVP) algorithm for estimating parameters in semilinear signals. They introduce a deflation technique for constraining the VPF to contain known basis vectors. For modeling exponential signals, the computational cost of the FNVP algorithm is shown to vary linearly with N, the size of the data vector, while other algorithms vary as N² or N log ₂ N