Estimation of the parameters of the map's projection using the trust region approach : modified More-Sorensen method
Abstract
Detection of the map's projection based on the trust-region strategy: the More-Sorensen method with the exact trust region step computation. Our software supports the detection of 5-9 parameters of the projection using the weighted non-linear least squares solution.
The exact computation of the trust region step is difficult, especially for cases, when the Hessian matrix B+lambda*I is negatively definite, which is referred as the hard case. In such situations, the Cholesky decomposition B+I*lambda = R'R can not be used, and the generalized vision, knowns as the Gill-Murray decomposition B+I*lambda+E = R'*R, comes on the scene.
The eigenvalues decomposition based on the QR factorization with the Wilkinson shift uses the tridiagonal matrix, constructed from the Lanczos biorthogonalization. The method is also applicable to early map geoereference.